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Essays on commercial media and advertising

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Essays on commercial media and advertising

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Content Essays on Commercial Media and Advertising by Yi Zhu A Dissertation Presented to the FACULTY OF THE USC GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (BUSINESS ADMINISTRATION) May 2013 Copyright 2013 Yi Zhu 1 DEDICATION I would like to dedicate this dissertation to my family, especially… my beloved wife, Linli Xu, for her infinite support, understanding and patience; my parent for instilling the importance of diligent work and persistence; and many friends for encouraging me to never give up my dreams. 2 ACKNOWLEDGEMENTS I owe my deepest gratitude to all of those people who have helped make this dissertation possible. I wish to thank, first and foremost, my two advisors, Dr. Anthony Dukes and Dr. Kenneth C. Wilbur, for their continuous help, guidance, smile, and patience. As mentors they were very generous with their time and knowledge and assisted me in each step to complete the dissertation. This dissertation would not have been possible without their inspiration and encouragement. I am also indebted to my committee members Dr. Shantanu Dutta, Dr. Lan Luo, Dr. Matthew Selove, and Dr. Guofu Tan for their very helpful insights, comments, discussions and suggestions during this process. 3 TABLE OF CONTENTS DEDICATION .............................................................................................................................................. 1 ACKNOWLEDGEMENTS .......................................................................................................................... 2 LIST OF TABLES ........................................................................................................................................ 5 LIST OF FIGURES ...................................................................................................................................... 6 ABSTRACT .................................................................................................................................................. 7 OVERVIEW ................................................................................................................................................. 8 CHAPTER ONE: HYBRID ADVERTISING AUCTIONS ....................................................................... 10 1. Academic Literature and Contributions .............................................................................................. 12 2. Key Assumptions and Empirical Support ........................................................................................... 16 2.1 Advertiser Types and Revenues .................................................................................................... 16 2.2 Advertiser Costless Effort and Click-through Rates ..................................................................... 18 2.3 Publisher Information ................................................................................................................... 21 2.4 Position Effects ............................................................................................................................. 23 2.5 Hybrid Advertising Auction Rules ............................................................................................... 24 3. The Dynamic Hybrid Advertising Auction ......................................................................................... 28 3.1 Profit Functions ............................................................................................................................. 29 3.2 Timing of the Game ...................................................................................................................... 30 3.3 Equilibrium Concept ..................................................................................................................... 31 4. Equilibrium Analysis .......................................................................................................................... 32 4.1 Publisher Expectations .................................................................................................................. 33 4.2 Advertisers’ Effort Levels ............................................................................................................. 35 4.3 Equilibrium Existence and Publisher Belief Uniqueness .............................................................. 38 4.4 Comparing the Hybrid Advertising Auction to the Generalized Second Price Auction ............... 39 5. Alternate Payment Schemes and Social Efficiency ............................................................................ 40 5.1 Efficient Allocation of Advertisers to Slots .................................................................................. 40 5.2 Nonexistence of Efficient Mechanisms without the UVDC ......................................................... 44 6. Discussion and Implications ............................................................................................................... 46 6.1 Conventional Wisdom in Hybrid Advertising Auctions ............................................................... 46 6.2 Should Publishers Offer Hybrid Advertising Auctions? ............................................................... 48 6.3 Historical Publisher Expectations ................................................................................................. 49 6.4 Public Policy Implications ............................................................................................................ 51 6.5 Maximizing Publisher Auction Revenues ..................................................................................... 52 4 CHAPTER TWO: THE SELECTIVE REPORTING OF FACUAL CONTENT BY COMMERCIAL MEDIA ....................................................................................................................................................... 54 1. Introduction ......................................................................................................................................... 54 2. The Model ........................................................................................................................................... 62 2.1 The State of the World and the Source of Facts ............................................................................ 63 2.2 Media Stances and Reports ........................................................................................................... 64 2.3 Consumer Demand ........................................................................................................................ 66 2.4 Game Timing ................................................................................................................................ 68 3. The Monopoly Medium ...................................................................................................................... 69 4. Competitive Media .............................................................................................................................. 76 5. Competition vs. Monopoly ................................................................................................................. 85 5.1 Media Informativeness and Factual Content Provision ................................................................ 85 5.2. Media Polarization ....................................................................................................................... 86 5.3 Media Bias and Media Competition ............................................................................................. 88 6. Implications and Discussions .............................................................................................................. 92 7. Conclusions & Limitations ................................................................................................................. 94 REFERENCES ........................................................................................................................................... 97 APPENDICES .......................................................................................................................................... 106 Appendix A ........................................................................................................................................... 106 Appendix B ........................................................................................................................................... 120 Appendix C ........................................................................................................................................... 121 Appendix D ........................................................................................................................................... 128 5 LIST OF TABLES Table 1. Summary of all Notation................................................................................................. 28 Table 2. A Numerical Example .................................................................................................... 65 6 LIST OF FIGURES Figure 1. Step 3 of 3 in Facebook’s “Create an Ad” Process ....................................................... 11 Figure 2. Google Help Page on Quality Scores for New Ads ...................................................... 23 Figure 3. Google Help Page on CPC/CPM Bid Competition ....................................................... 25 Figure 4. Google Help Page on Quality Scores and Ad Rank Formulas ...................................... 25 Figure 5. Facebook CPC/CPM Help Page .................................................................................... 26 Figure 6. Less-Than-Fully Informative Equilibrium with x Intervals .......................................... 72 Figure 7. The Uninformative Equilibrium .................................................................................... 73 Figure 8. A Partially Informative Equilibrium ............................................................................. 74 Figure 9. Uninformative Equilibrium with Two Media................................................................ 84 Figure 10. Media Bias in Monopoly under Different Informative Level ..................................... 89 Figure 11. Media Bias Comparison under Competition (z and M are large) ............................... 92 7 ABSTRACT My dissertation aims to advance our understanding of marketing processes in light of the emerging new media and technology. My dissertation first provides guidance on how websites should offer sponsored-links services with new hybrid advertising auctions mechanism. Facebook and Google offer hybrid advertising auctions that allow advertisers to bid on a per-impression or a per-click basis for the same advertising space. This chapter studies the properties of equilibrium and considers how to increase efficiency in this new auction format. Rational expectations require the publisher to consider past bid types in order to prevent revenue losses to strategic advertiser behavior. The equilibrium results contradict publisher statements and suggest that, conditional on setting rational expectations, publishers should consider offering multiple bid types to advertisers. The second chapter of my dissertation examines factual content production in commercial media and provides insights into a wide variety of settings, including user-generated content (UGC), daily news, and product reviews. Commercial media supply factual content to consumers who pay for facts to learn about the state of the world (the state). If media take stances that closely reflect the actual state, they can provide many facts. But, if consumers also value content that matches their opinions, media may want to slant their stances away from the state, which limits the number of facts they can report. We find that competitive media leave consumers knowing less by providing fewer facts. We also find that a monopoly medium may be more polarizing than competitive media. 8 OVERVIEW The rise of digital technologies and new media has been reshaping the ways in which businesses can market to consumers. Consumers have access to more sources of information, while businesses have better knowledge about consumers’ decisions. It remains unclear, however, how consumers and firms will react to these changing conditions. This fascinating trend opened my eyes to the field of marketing research and motivated my dissertation in studying the interactions among online advertising, technology advancement and new media. My dissertation aims to advance our understanding of marketing processes in light of these emerging new media, with the essential goals of improving our understanding of the market place and offering insightful implications to marketers to make better decisions. The first chapter of my dissertation, “Hybrid Advertising Auctions,” examines the properties of equilibrium and considers how to increase efficiency in search advertising under the new hybrid auction format, in which publishers allow advertisers to bid on a per-impression or a per-click basis for the same advertising slot on the platform. The equilibrium results contradict the publisher’s statements. It suggests that publishers should consider offering multiple bid types conditional on setting rational expectations. Without this deterrence, brand advertisers could calibrate high click-through expectations by using per-impression bids in conjunction with high click-through rates and then profit by switching to per-click bids with low click-through effort to reduce advertising costs. It further provides implications to publishers on how to design a more efficient payment scheme to achieve social optimum. The second chapter of my dissertation, “The Selective Reporting of Factual Content by Commercial Media,” studies the impact of competition on the amount of factual content that commercial media supply to consumers. The internet and mobile technology have made it easier 9 and cheaper to distribute factual content. Newspapers, magazines, radio stations and television networks distribute factual content through the internet and mobile devices. In addition, there are thousands of online-only distributors of content as well (e.g. slate.com), not to mention the countless number of bloggers who provide factual content for commercial gains. The emergence of these technologies has, consequently, increased competition for readers’ attention. The central question we ask in this chapter is whether this increase in competition corresponds to an increase in the provision of factual content? In our model, the commercial media could choose to report the actual state of the world by providing many facts, but they would also have incentives to slant their stances to match consumers’ prior opinion. Hence this paper extends the classic cheap-talk framework by incorporating two features: (1) Consumers prefer reading more facts; and (2) consumers have the ability to infer the state of the world from the stances taken by the media. Contrary to the seemingly intuition that competition should encourage media to be more informative with more facts, this chapter instead shows that competitive media leads consumers knowing less by providing fewer facts on average and a monopoly medium might be more polarizing than competitive media. 10 CHAPTER ONE: HYBRID ADVERTISING AUCTIONS Auctions are the dominant sales mechanism to allocate online advertising space. The ascendance of internet auctions has been matched by a growing importance in the literature (Chen and He 2006, Goldfarb and Tucker 2007, 2009, Katona and Sarvary 2008, Yao and Mela 2009). One type of auction is the cost per thousand impressions (CPM) auction in which advertisers bid for impressions and pay each time their ad is displayed on a webpage. CPM ad pricing is dominant in the market for internet display advertising. Another type of auction is the cost per click (CPC) auction in which advertisers bid for clicks and pay only when their ad is clicked. CPC ad pricing is dominant in the market for internet search advertising. This paper analyzes the hybrid advertising auction, in which each advertiser must choose whether to use CPC bidding or CPM bidding. Bids of both types compete for the same advertising space. Two major websites, Facebook and Google, currently use hybrid auctions. In August 2010, Facebook was the most visited site on the internet: 500 million people used it for 46 minutes per day on average, with half of the users logging in every day (Facebook 2010). It was believed that Facebook earned about $700 million in advertising revenues in 2009 (Eldon 2010). Figure 1 shows that Facebook advertisers are required to choose a CPC or CPM option to bid for ad space on the site. Google uses the hybrid auction to allocate ad space on its content network, which generated $7.2 billion in 2008, 30.5% of the company’s advertising revenues (Google 2010). However, Google does not offer CPM bidding for ads displayed next to its search results. In principle, any seller of online advertising could use a hybrid auction to sell advertising space. 11 Figure 1. Step 3 of 3 in Facebook’s “Create an Ad” Process This paper has two goals. The first is to understand the properties of equilibrium in this new auction format. The second is to consider how advertising sellers ( “publishers”) might offer advertisers more efficient mechanisms within the class of hybrid auctions. The model features brand advertisers and direct response advertisers competing for a set of ad slots sold by a publisher. In each period, each advertiser chooses its bid type, bid level, and whether to maximize click-through rates. The publisher chooses its click-through rate expectations without knowledge of advertisers’ types. The results show how the publisher can use its click-through expectation to deter a type of moral hazard on the part of brand advertisers. Without this deterrence, brand advertisers could calibrate high click-through expectations by using CPM bids in conjunction with high click-through rates and then profit by switching to CPC bids with low click-through effort to lower advertising costs. The analysis here is somewhat general compared with much of the literature: it allows for a potentially large number of slots, many bidders, private information and repeated interactions. 12 This paper derives several results of managerial interest, but the implications might matter most to those publishers—such as AOL, Microsoft, MySpace, and Yahoo—that do not currently offer hybrid advertising auctions. These firms do not have the benefit of experience to inform a major change in their business model. Auction revenues depend critically upon competition within the auction, so if offering multiple bid types can increase the number of bidders a platform attracts, its effect on publisher revenues may be substantial. The next section discusses the academic literature to which this paper contributes. Section 2 presents the model’s major assumptions. Section 3 outlines the game, and section 4 analyzes its equilibrium. Section 5 considers socially optimal payment schemes within the class of hybrid auction mechanisms. Section 6 concludes with managerial implications and directions for future research. 1. Academic Literature and Contributions This paper adds to a quickly growing literature on online advertising. The pioneering treatments on equilibria in search advertising auctions are Edelman et al. (2007) and Varian (2007), which independently studied aspects of the auction mechanisms used by Google and Yahoo (known as the “Generalized Second Price” auction, or “GSP”). The GSP does not have a strictly dominant bidding strategy, but under intuitive refinements advertisers with higher expected valuations per click occupy higher ad positions in equilibrium. Athey and Ellison (2008), Chen and He (2006), and Xu et al. (2009) studied how advertisers’ bids are affected by interadvertiser competition. Recent analytical work has examined such topics as how to incorporate searcher and keyword characteristics into the advertising auction (Even-Dal et al. 2008); how CPC advertising auctions affect advertising’s quality-signaling function (Feng and Xie 2007); the interplay between 13 organic and sponsored search links and the publisher’s optimal choice of paid links (Katona and Sarvary forthcoming); how to modify the position auction to account for externalities between advertisers at different positions (Kempe and Mahdian 2007); how to distribute available advertising space among bidding advertisers (Chen et al. 2009); and the effects of “click fraud” on search engine revenues (Wilbur and Zhu 2009). There is also a rapidly expanding collection of empirical studies of search advertising markets. Ghose and Yang (2009) find that click-through and conversion rates decrease with ad position and that search engines account for both current bid price and prior click-through rates when allocating advertisements to ad slots. Goldfarb and Tucker (2007) find that pricing search advertisements separately across different keywords allows search engines to price discriminate among advertisers. Rutz and Bucklin (2007a) show how to borrow information across a large number of keywords and regions in order to solve the optimal keyword selection and bidding problem. Rutz and Bucklin (forthcoming) show that while generic keywords (e.g. “hotel los angeles”) are often very expensive, they have spillover effects as consumers tend to begin shopping with a generic search and later use a cheaper branded search to purchase. Yao and Mela (2009) use a structural dynamic Bayesian model to analyze data from a product search engine. Among many findings, their study reports that frequent clickers place a greater emphasis on the position of the sponsored advertising link. They also find that a switch from a first-price to a second-price auction yields advertiser bids that are in line with willingness to pay, but this switch has a small impact on search engine revenue. Goldfarb and Tucker (forthcoming) provide evidence that both advertising targeting and obtrusiveness increase consumers’ purchase intentions when used alone, but interact negatively when used together. 14 Several recent papers examine questions similar to those posed here. Goel and Munagala (2009) propose a mechanism in which the publisher requires each advertiser to enter both a CPM bid and a CPC bid. The extra information transferred by the advertisers to the publisher raises the publisher’s revenue by allowing it to construct more efficient rankings. The fundamental difference in their paper is that they propose a new hybrid advertising auction mechanism which requires advertisers to enter two bids, whereas this paper analyzes single-bid auction mechanisms already in use. While the focus here is on hybrid advertising auctions with CPC bidding and CPM bidding, a third bid type is the cost per action (CPA) model in which advertisers pay per purchase or lead. CPA bidding is used less frequently than CPC or CPM bidding (Nazerzadeh et al. 2008). The analysis below can be reinterpreted as a CPM/CPA hybrid advertising auction if one assumes that advertisers are choosing their conversion rate rather than their click-through rate. Edelman and Lee (2008) independently analyze a CPC/CPA hybrid advertising auction. They focus on characterizing equilibrium bids under intuitive refinements of the model and show that the publisher is weakly better off when it offers multiple types of bid to advertisers. Hu et al. (2010) shows that CPC and CPA pricing models may conflict due to unobservable, non- contractible effort and adverse selection between brand and direct response advertisers. Hu (2004) used a contract theory approach to show that performance-based pricing can align publisher and advertiser incentives when complete contracts are infeasible. Agarwal et al. (2009) describe a number of counterintuitive features of CPA auctions in contrast with CPC auctions. Jerath et al. (2010) study how a platform’s choice of either a pure CPC or a pure CPM auction influences auction competition and resulting clicks. This work is also related to the literature on pay-per- lead and pay-per-conversion pricing in affiliate marketing, e.g. Libai et al. (2003). 15 The analysis in this paper is also related to signaling models. These were introduced as a possible resolution to inefficiency induced by asymmetric information. For example, in the classic labor market example of Spence (1973), a firm is willing to pay a higher wage to a good employee than a bad employee. However, the firm cannot identify employee type prior to hiring in the absence of a signal. The good employee has a lower cost of completing education, so she engages in additional years of schooling to signal her type to the employer. This general modeling framework has been to study such marketing questions as the role of demand signaling in distribution channels (Chu 1992, Desai 2000), how price advertising impacts consumers’ store price expectations (Simester 1995, Anderson and Simester 1998), and how uninformative advertising and money-back guarantees influence product quality perceptions (Mayzlin and Shin 2009, Moorthy and Srinivasan 1995). The asymmetric information in our setting lies in the purpose of a new advertising campaign. The advertiser knows whether it is intended for branding or direct response purposes, but the publisher does not. Despite the presence of asymmetric information, there are two main differences between the model analyzed here and a typical signaling model. First, there is no assumption of a costly signal sent from the advertiser to the publisher. The publisher is able to mitigate all harmful effects of asymmetric information without requiring the advertiser to invest resources in a signal. Second, the problem of asymmetric information considered here may persist in many periods, whereas most signaling models assume static games. For example, the inefficiency in the example above may be mostly resolved if the firm hires the employee for a probationary period which is long enough to determine her type. These two points highlight the differences between the current analysis and a standard signaling model. 16 This paper’s primary contributions are to make a first statement about equilibrium strategies in hybrid advertising auctions and to develop an understanding of how to reach socially efficient outcomes in these auctions. The analysis differs from most of the literature in several key assumptions. It considers advertiser competition in type of bid as well as bid level and allows for advertiser heterogeneity in payoff function as well as reservation price. It does so under the realistic assumptions of repeated interactions and private information about advertisers’ types, profits, and click-through rates whereas most of the literature considers static models of perfect information. 2. Key Assumptions and Empirical Support The model makes several key assumptions, which are motivated by real-world behavior. This section describes those assumptions, their support, and their impact on the results. 2.1 Advertiser Types and Revenues There are two types of advertising campaigns: direct response and brand-focused. Direct response advertising seeks to stimulate immediate action, such as online purchases. Examples include large online merchants, like Amazon.com and eBay.com, purchasing targeted ads related to the brands and products they sell. Many offline businesses, such as mortgage brokers or law firms, engage in direct response advertising to generate registrations or sales leads. The ascendancy of the Google Adwords platform is generally attributed to its usefulness to direct response advertisers. Brand advertising seeks to influence consumers’ product perceptions by increasing awareness or influencing consumer attitudes. It is often employed to alter consumer decisions 17 made in offline environments, such as retail stores. Examples of brand advertising may include a consumer package goods brands such as Scott paper towels, or a luxury brand such as Gucci, seeking to influence consumers’ brand associations. Publishers typically do not know the purpose of individual campaigns. Online advertising is typically allocated to large numbers of advertisers via self-service automated processes. It would likely be expensive and perhaps impossible to verify manually whether each advertiser is a brand or direct response advertiser. Even if the publisher attempts manual verification of advertiser types (e.g., having a human employee visit each advertiser’s website), it may not have enough information to discern those types perfectly, since a single advertiser’s goals may vary from campaign to campaign. For example, Coca-Cola may seek to shape brand associations in one campaign; in another, it may seek to increase online enrollments in its “Coke Rewards Points” loyalty program. Publisher uncertainty about campaign purpose is the source of asymmetric information in the model. To formalize these assumptions, we model a set of i=1…N risk-neutral advertisers bidding for N K k   ... 1 ads offered by a publisher in each of t=0,…,T time periods. 1 There exist a set of brand advertisers B and a set of direct response advertisers D. Type B’s payoff depends on exposures while type D’s depends on clicks. Brand advertiser i’s profit per exposure is B Bi F r ~ where B F is a cumulative distribution function defined on the interval ) , 0 (  . Direct response advertiser i’s profit per click is D Di F r ~ where D F is a cumulative distribution function defined on the interval ) , 0 (  . 2 1 Our assumption that N K  is in keeping with the literature and rules out the case of multiple slot purchases by a single advertiser, greatly simplifying the analysis. In practice, the publisher controls K and therefore can set it equal to N when the number of bidders is less than the number of available ad slots. 2 We have also solved models where each advertiser is characterized by a value for an ad exposure and a value for an ad click. The results in section 4 go through mostly unchanged, but the case of discrete advertiser types is simpler. 18 2.2 Advertiser Costless Effort and Click-through Rates Advertisers may influence click-through rates. As a very simple example, they can choose to encourage consumers to “click here.” Another possible strategy is to include a “hard sell” in the ad, which might be effective in shaping offline behavior but might discourage the consumer from clicking the ad. A third option is to alter the frequency with which new ads are introduced, which in turn may influence the likelihood of consumer clicks. Many empirical studies support this assumption. Krishnamurthy (2000) suggested the primary factors determining consumer response to banner ads are color, interactivity, and animation. Lohtia et al. (2003) confirmed that these factors, along with emotion, influenced consumers’ ad response in a field study of 8,725 banner advertisements in both B2B and B2C settings. Robinson et al. (2007; see also many references therein) found that increasing the number of words in a banner ad from less than 6 to more than 15, holding other factors constant, can increase the click-through rate by more than 100%. Chandon et al. (2003) found that advertisement size, animation, and phraseology (e.g., “click here” or “online only”) significantly influenced click-through rates; see also Baltas (2003). Yaveroglu and Donthu (2008) find that ad repetition has a significant effect on consumers’ intent to click. Ghose and Yang (2009) show that click-through rates depend on whether an ad contains retailer or brand information. A full review of this literature is beyond the scope of this article, but there is broad agreement that advertisement content influences consumer response to online advertising. In addition to academic work, many sellers of online advertising offer tips on how to design ads to maximize click-through rates. They offer tools that facilitate experimentation to see 19 which ads generate the highest click-through rates. An advertiser willing to expend costless effort to maximize its click-through rates could choose to employ strategies from a wide range of studies, seller-generated tools, and its own experience. 3 Could an online advertisement that generates a low click-through rate be profitable to a brand advertiser? Several studies support the idea that online advertisements with low click- through rates can be effective in building brands. Dré ze and Husherr (2003) show that despite high rates of “ad-blindness” (consumers’ tendency to avoid focusing on the parts of webpages where ads appear), consumers exposed to banner ads exhibit higher rates of aided and unaided brand recall regardless of whether they clicked the ads or not. Danaher and Mullarkey (2003) demonstrate that time spent viewing a webpage increased the likelihood a consumer would recall a brand whose banner ad appeared on that webpage. Advertiser i's click-through rate is modeled as it i i it x      . (1) ) 1 , 0 (  i  is advertiser i's baseline click-through rate, which is determined by such exogenous factors as brand recognition and the match between the advertiser’s webpage and the search term. it x is a dummy variable which indicates whether advertiser i exerts costless effort to maximize its click-through rate in period t, and ) 1 , 0 ( i i     is the advertiser-specific productivity of exerting costless effort. The advertiser chooses whether to exert costless effort ( 1  it x ) or not ( 0  it x ). It is possible to understand this distinction by looking at an advertisement and trying to discern its 3 A recent study indicates that the percentage of consumers who click on at least one ad in a month fell from 32% in July 2007 to 16% in March 2009, and that 67% of all ad clicks come from just 4% of consumers (Loechner 2009). If this ‘clicking segment’ is sufficiently homogeneous, it may become progressively easier for advertisers to choose ad copy to influence clicking probability. 20 purpose. If the ad copy takes the central route to persuasion (Tellis 2004), it is more likely that the advertiser is trying to generate clicks. Clicking is a conscious behavior, so rational arguments (like “free”) will likely be more effective in generating this conscious behavior. If, on the other hand, the ad copy takes the peripheral route to persuasion, one might expect it to be a low-effort advertisement. An ad that does not try to engage the rational mind is less likely to generate a rational response like a click. This ad still may be of value to a brand advertiser by influencing consumers’ latent attitudes and associations. That many online ads appear next to articles, blog posts, or social network content, often in places to which consumers do not pay conscious attention, suggests that quite a bit of display advertising may work by avoiding the central route to persuasion. One could instead make it x continuous or nonlinear. This would not change the primary results because costless effort will always lead advertisers to maximize or minimize effort within the range of feasible values. If effort is binary but costly, the results, again, will be mostly unchanged. Since advertising effort is a fixed cost, changing this cost only affects investments by firms whose advertising profits are relatively small, similar to changing the fixed cost of production in a standard model of oligopolistic price or quantity competition. One could also consider an exposure rate variable to allow advertisers to invest effort to increase the probability a consumer is exposed to their ad. The main reason to leave this out is that, while clicks can be easily tracked, currently consumer exposures can only be measured with eye-tracking technology. Such technology is not widely deployed, so advertisers’ investments in exposure probabilities have limited effect on advertising costs or publisher revenues. Note that all click-through-related variables are advertiser-specific. It is natural to think that direct response advertisers would likely have higher baseline click-through rates and higher 21 returns to effort. No such distinction among advertiser types is made here, but the model is fully general and can easily be made more specific to accommodate such an assumption. 2.3 Publisher Information We assume the publisher knows i  and i  . In general, the publisher likely has good information about click-through since it has data on many advertisers and campaigns. Each advertiser, on the other hand, typically only has information from its own past campaigns. The results presented in this paper do not require any advertiser knowledge of i  or i  . Advertisers, however, determine whether they exert costless effort to maximize click- through rates. Since this may vary from ad to ad, the publisher must anticipate effort levels. E it  denotes the publisher’s expectation of advertiser i's click-through rate in period t. A publisher may not observe an advertiser’s effort before the ad runs, but it may observe clicks after the ad starts running. It is likely that consumers are heterogeneous and that consumer response to ads may be stochastic. Therefore, it would take the publisher some period of time both to deduce signal from noise and to learn each advertiser’s effort level with some predetermined degree of precision. The minimum amount of time needed to measure all advertisers’ costless effort levels at some confidence level is the duration of one “period” in the repeated game. If click-through rates are sufficiently low, or if they are sufficiently noisy, then this duration may be of some considerable length. There are three ways that publishers may anticipate effort levels. The first is through past experience. A publisher is able to observe when an advertiser alters an ad. Consider the following scenario: advertisers bid and enter a set of ads W in period t. By the end of period t, the publisher has observed the effort level associated with each ad in W. If the same set of ads is 22 entered in period 1  t , the issues described in this paper will not apply in period 1  t . Therefore, the scope of the analysis is any period in which the set of ad creatives has changed from the previous period. Yet this scope may still be considerable in magnitude, since the number of keywords sold is very large, the duration of a single period may be considerable, and the number of ads entered by a single advertiser may be large. If the publisher has imperfect information about an advertiser’s ad quality, and if that state of imperfect information is beneficial to the advertiser, the advertiser is likely to alter its ad creatives quite frequently in order to increase the frequency with which the publisher has imperfect information. 4 This is made even more likely by advertisers’ ability to use software to generate ad creatives. The second way in which a publisher can anticipate advertiser costless effort is to analyze the text or graphic content of the ad algorithmically and predict consumer response based on these “creative” elements. There are several reasons to think this is technically infeasible. First, some publishers say they do not do this. For example, Google states in Figure 2 that its “Adwords system treats an edited ad like it’s brand new and has no performance history.” Second, if it were feasible, the publisher could suggest the click-maximizing ad text to any individual advertiser. No publisher currently offers this, though doing so would likely increase publisher revenues. If a publisher was able to produce this technology, the asymmetric information which motivates this paper would be fully resolved. However, as shown below, it is possible to fully mitigate any negative effects of strategic behavior of this asymmetric information even in the absence of this technology. 4 A counterargument would hold that the publisher could mostly deter this behavior by limiting the number of new ads an advertiser may use. The advertiser could circumvent this policy by opening multiple accounts. As long as advertiser identity is imperfectly observable, there is a threat of frequent ad introductions. 23 Figure 2. Google Help Page on Quality Scores for New Ads The third way to anticipate advertisers’ choices of costless effort levels is to use economic reasoning; that is, to consider advertisers’ equilibrium strategies. This is basically costless to the publisher. Section 4.1 proposes a way to do this. 2.4 Position Effects Following Katona and Sarvary (2008), an ad appearing in slot k has a position-dependent click-through multiplier k X with 0 ... 1 2 1      K X X X . Position-dependent exposure multipliers 0 1 2 1      K Y Y Y  allow an ad’s position on the page to determine the likelihood that it is seen. It is necessary to define “page views,” “exposures,” and “impressions.” A page view occurs when a consumer loads a webpage containing a set of ads. An exposure or impression occurs if the consumer processes an advertisement. In other words, a page view is a potential exposure or a potential impression. As discussed above, individual exposures are unobserved without eye-tracking technology. The measure of available consumer page views is normalized to 1 without loss of generality. 24 2.5 Hybrid Advertising Auction Rules Assumptions about how the hybrid advertising auction works are based on (1) logic; (2) previous academic literature that has examined related auctions; and (3) public statements by companies that currently offer hybrid advertising auctions. Assumption 1 The publisher allows each advertiser i to enter either a CPC bid c it b or a CPM bid m it b in each period t and assigns advertisers to slots in order of total expected advertiser willingness to pay. If advertisers were charged their bids, an advertiser i with a CPM bid m it b would pay m it k b Y for slot k. If i instead entered a CPC bid c it b , its total expected payment for slot k would be c it E it k b X  . Assumption 1 implies that if advertiser i enters a CPM bid and advertiser j enters a CPC bid, i will be allocated to slot k and j to a less desirable slot if c jt E jt k m it k b X b Y   . Assumption 1 is consistent both with Google’s statement in Figure 3 that “neither type of ad [CPC or CPM] has a special advantage over the other,” and with Google’s ad rank disclosures shown at the bottom of Figure 4. It is also consistent with Facebook’s statement in Figure 5 that “for any available ad inventory, Facebook selects the best ad to run based on the cost per click or impression and the ad performance.” If the publisher used any other ranking method, it would systematically bias advertisers toward using one type of bid over the other. 25 Figure 3. Google Help Page on CPC/CPM Bid Competition Figure 4. Google Help Page on Quality Scores and Ad Rank Formulas 26 Figure 5. Facebook CPC/CPM Help Page Assumption 2 Each advertiser is charged the minimum amount necessary to keep its place in the ranking. Assumption 2 is in line both with the prior literature on CPC auctions (e.g. Edelman et al. 2007, Varian 2007 and 2009), and with the common understanding of Google’s pure-CPC keyword auction. As Google states in Figure 2, “No matter which type of ad [CPC or CPM] wins the position, the Adwords discounter monitors the competition and ensures that the winning ad is charged only what is necessary to maintain its ranking above the next-highest ad.” Assume advertiser i holds position k and advertiser j holds position k+1. Assumptions 1 and 2 imply that if both advertisers entered CPM bids, then i pays m jt k b Y total. If both advertisers entered CPC bids, then i pays E it c jt E jt b   per click. If advertiser i entered a CPC bid and j entered a 27 CPM bid, then i pays E it k m jt k X b Y  per click. If i entered a CPM bid and j entered a CPC bid, then i pays c jt E jt k b X  . To simplify advertiser profit functions in the next section, we write the CPM payment or the expected CPC payment of the advertiser in slot k in period t as         bid. CPM a submits 1 slot in advertiser if , bid. CPC a submits 1 slot in advertiser if , ' ' ' k i' b Y k i' b X C m t i k c t i E t i k kt  We further assume that an advertiser only changes its bid type or effort level if it benefits from doing so. This assumption is consistent with any arbitrarily small nuisance cost of changing the bid type or effort level. It is a tie-breaking rule and can be thought of as “advertiser inertia.” Pauwels (2004) finds that firms exhibit inertia in tactical decisions such as pricing and promotions even when inertia reduces profits. The advertiser inertia assumption is weaker than Pauwels’ result, since it only presumes inaction when action cannot increase profits. The role of this assumption rules out degenerate expectation functions in the proof of Proposition 1. This section closes with an observation and an associated assumption. Conditional on an equilibrium assignment, it is possible for the publisher to increase click-through expectations to increase higher advertisers’ payments without changing the equilibrium assignment. Consider a simplified example to understand this action. Suppose a seller is offering one item to two bidders with privately held valuations of $2 and $1. The seller could use a mechanism such that (1) each bidder enters a bid and (2) after observing the bids, charge the higher bidder one penny less than her bid. This would result in revenues of $1.99, rather than the second-price auction payment of $1. In our setting, the publisher could achieve a very similar effect by manipulating click-through expectations to reduce the difference between advertisers’ expected willingness to pay. We assume the publisher does not do this for several reasons. First, it may be constrained by legal 28 contracts or the threat of a class-action lawsuit. Second, it would likely reduce advertiser participation in the auction by reducing advertiser surplus. Third, it may be perceived as “unfair” and damage the publisher’s reputation. Fourth, we know of no theoretical auction paper that considers strategies of this type. 3. The Dynamic Hybrid Advertising Auction This section presents remaining model assumptions. Table 1 summarizes all notation. Table 1. Summary of all Notation. Symbol Definition i  Minimal click-through rate for advertiser i it x =1 if advertiser i exerts costless effort to maximize click-through rate in period t; =0 otherwise i  Marginal number of clicks produced by advertiser i’s costless effort E it  Publisher’s expectation of advertiser i’s click-through rate in period t it g =c if advertiser i enters a CPC bid in period t =m if advertiser i enters a CPM bid in period t it g it b Advertiser i’s bid of type it g in period t k X Slot-dependent click-through multiplier k Y Slot-dependent exposure multiplier Bi r Reservation value per click of brand advertiser i Di r Reservation value per click of direct response advertiser i B F CDF of brand advertisers’ reservation values 29 D F CDF of direct response advertisers’ reservation values ikt R Total revenues of advertiser i in position k in period t kt g it C it  Total cost of position k to advertiser i in period t it g ikt  One-period profits of advertiser i in position k in period t  Discount rate a i  Discounted sum of advertiser i’s expected profits in all periods p  Discounted sum of publisher’s expected profits in all periods  Possible publisher expectation function it H Vector of advertiser i’s past bid types up to period t and efforts up to t-1 T Total number of periods. 3.1 Profit Functions For simplicity, advertiser reservation values ( Bi r and Di r ), baseline click-through rates ( i  ), and returns to costless effort ( i  ) do not change over time. Total revenues according to advertiser identity, type, and position are ikt R . Let } , { m c g it  indicate bid type (CPC or CPM), and         c g γ γ m g it E it it it g it if if 1  (5) so that the one-period profits of advertiser i in slot k in period t can be written as kt g it ikt g ikt C R it it     . (6) Define N-vectors N i it t g g ,..., 1 ) (   , N i g it t it b b ,..., 1 ) (   , N i E it E t ,..., 1 ) (     , N i it t x x ,..., 1 ) (   and N i g it t it ,..., 1 ) (     . The discounted sum of expected advertiser profits is 30       T t g it E it g it it ikt t b x g a i it it it g it it it b b x 0 } { }, { }, { ) , , ( E max E    (7) where  is the discount factor and it g it b   is an (N-1)-vector of other advertisers’ bids in period t. The publisher’s one-period profits are the sum of payments that advertisers make for all occupied slots, so the discounted sum of expected publisher profits is       T t K k t t kt g it p x b C it E t 0 1 t ] , [ E max E    . (8) 3.2 Timing of the Game This paper analyzes a repeated game with private information because online advertising auctions are repeated with high frequency. Results that hold in a static model might not hold in a more realistic dynamic setting. Within each period t, three sets of strategic actions are taken: advertisers choose bids (types and amounts), the publisher sets click-through expectations, and advertisers choose costless effort levels. After all actions are taken, the publisher’s mechanism assigns advertisers to slots, consumers click ads, advertiser profits are realized, and transfers are made from advertisers to the publisher. This paper’s results require two assumptions regarding timing. The first assumption required for the results below is that the publisher does not observe whether the advertiser has exerted costless effort to maximize click-through rates prior to the assignment of advertisements to slots. This assumption preserves the moral hazard nature of the publisher/advertiser interaction. The full justification for this assumption is in section 2.3. Second, it must be the case that the publisher does not finalize its click-through expectations until after it observes advertisers’ bids. This is necessary because the publisher must 31 form expectations about every advertiser that joins the auction, and it only knows which advertisers are in the auction after the advertisers enter their bids. This is feasible for three reasons: (1) the publisher controls the computer system into which bids are entered; (2) the publisher controls the time lag between when bids are entered and when they affect the ad rankings; and (3) publishers’ software can form click-through expectations reasonably quickly. If this assumption is violated, the publisher will not be able to use any information about an advertiser’s bid to set click-through expectations. Thus, bids must be entered before click-through expectations are formed, and click- through expectations must be formed prior to effort variables being revealed. Any sequence of actions meeting these requirements will produce the results below. It is perhaps simplest to think of this as a two-stage game within each period t. First, advertisers simultaneously enter bids and choose costless effort levels. The publisher then observes the bids, but not the effort levels, and sets its click-through expectations. 3.3 Equilibrium Concept The equilibrium concept concludes the specification of the game. Definition 1 A Perfect Bayesian Nash Equilibrium is defined by any set of publisher expectations  function about advertisers’ click-through rates T t E t ,..., 0 ) (   , any set of bids T t t b ,..., 0 ) (  , and any set of costless effort levels T t t x ,..., 0 ) (  for which the following conditions hold: 1. Incentive Compatibility: the choice sequence of costless effort levels ( iT i x x , , 0  ) and bids ( iT i g iT g i b b , , 1 0  ) maximize expected profits a i  E for all advertisers i=1,…,N. 32 2.Individual Rationality: for any advertiser i who wins slot k in period t, 0 E  it g ikt  . 3. Publisher Optimality: the choice of expected click-through rates T t N i E it ,..., 0 , ,..., 1 ) (    maximize expected profits p  E . 4. Consistency of Publisher Beliefs: the publisher updates its belief using players’ observed actions. For any publisher expected click-through rate function  , ) | , Pr( ) | , Pr( ) | , Pr( ) , | Pr(                it i it it i i it it i i it it i i E it H H H H          for all n i ,..., 1  . and T t ,..., 1  , where it H contains advertiser i’s past bids up to and including period t and past click-through rates up to period t-1. The first condition ensures that each advertiser chooses its bid type, bid level, and costless effort level in each period to maximize long-run profits. The second condition is a standard individual rationality constraint ensuring nonnegative profits for winning advertisers. The third condition ensures that the publisher sets rational expected click-through rates. The fourth condition means the publisher belief about advertisers’ click through rate is correct in equilibrium for every period after the start of the campaign. The fourth condition is a standard in perfect Bayesian equilibrium analysis. 4. Equilibrium Analysis This section characterizes equilibrium. It proves that equilibrium exists and that the publisher has a unique expectation function that prevents advertisers from reducing cost through strategic choice of bid types and effort, but this leads to the counterintuitive result that direct response advertisers always use CPM bids. Finally, it compares the hybrid auction with the Generalized 33 Second Price (GSP) auction to show that any GSP equilibrium can be supported in the hybrid auction format. Equilibrium is determined by the interplay of advertisers’ strategies and publisher expectations. We first characterize publisher expectations and then derive equilibrium advertiser choices of bid types and effort under that expectation function. Then, given equilibrium advertiser strategies, Proposition 1 shows that equilibrium exists and the expectation function is unique. 4.1 Publisher Expectations Publisher expectations are critical in order to produce the optimal assignment of advertisers to slots. They affect advertisers’ costs, which in turn determine advertisers’ optimal bid types. The publisher must use its effort expectation function to prevent advertisers from “gaming the system.” The threat the publisher faces comes primarily from brand advertisers, who by definition do not care about clicks. This risk arises because the publisher must assign advertisers to slots prior to observing their costless effort levels. The risk is that a brand advertiser may use high effort levels in conjunction with CPM bidding to lead the publisher to expect a high effort level. The CPM bids would ensure that the advertiser does not pay any additional cost in connection with the high effort levels. Then, the brand advertiser could take advantage of the high click-through expectation to gain a cost advantage. It could do this by switching to a CPC bid with a low effort level in order to reduce its total payment for the same advertising space. 34 However, the publisher has a tool at hand. Advertisers’ bids must precede the assignment of advertisers to slots. Therefore the publisher may base its expectations on the type of bid the advertiser enters. Since profitable effort reversals of the type described above require switching bid types from one period to the next, the publisher has an “early warning system.” A publisher belief function that punishes an advertiser for switching bid types can prevent such opportunistic behavior. This gives rise to Bayesian Publisher Expectations, as formalized in Definition 2. Definition 2 Bayesian Publisher Expectations (BPE) imply the publisher’s click-through expectations are based on past bid types:            otherwise ] , 0 [ any for if or 0 if 1 it s it i E it t s c g t    . (9) BPE says that the publisher will expect all advertisers to exert low effort at the beginning of the game. It will only come to expect high effort after an advertiser has calibrated that expectation by exerting high effort in the previous period. Lemmas 1 and 2 below show that direct response advertisers will always exert high effort under BPE, while brand advertisers will be indifferent between high effort and low effort. Proposition 1 establishes that Bayesian Publisher Expectations uniquely maximize publisher profits in equilibrium. The advertiser strategy described above is a multi-stage strategy in which the advertiser invests with a CPM bid to calibrate high click-through expectations and a CPC bid to profit from those heightened expectations. Therefore BPE requires the publisher to expect low effort from an advertiser if it ever uses a bid type that indicates a payoff behavior. This is similar to a “grim trigger strategy” studied in the context of a repeated prisoner’s dilemma game (e.g., Osborne 35 2004). If a strategic player can successfully commit to punish another player’s action indefinitely, it can deter the other player from taking such an action. Another way to understand BPE is to relate it to “Gresham’s Law,” or “bad money drives out the good.” Since low effort may yield a cost advantage under CPC bidding, the publisher has no choice but to assume every advertiser using a CPC bid will enter a low click-through rate. This leads all direct response advertisers to optimally use CPM bids, as shown below. 4.2 Advertisers’ Effort Levels Publisher expectations in Definition 2 allow for some clear statements about advertiser behavior. We proceed by analyzing advertiser effort levels conditional on choice of bid type in Lemmas 1 and 2. Lemma 3 then characterizes optimal bid type choices. After solving for optimal advertiser actions conditional on publisher beliefs, Proposition 1 shows that BPE uniquely maximizes publisher revenues. Lemma 1 The dominant strategy for any direct response advertiser under BPE is to choose a high effort level. Lemma 1 ensures that direct response advertisers will maximize their click-through rates in all periods, since clicks directly increase their revenues. Any rational bid that allocates a direct response advertiser to an ad slot is one that gives the advertiser a positive profit per click; therefore the advertiser will always seek to get as many clicks as it can. This ensures that the proposed definition of Bayesian Publisher Expectations does not harm this core constituency of advertisers. 36 Next, consider brand advertisers’ effort levels. Lemma 2 Any brand advertiser entering a CPM bid under BPE is indifferent between high effort and low effort. A brand advertiser entering a CPC bid will exert low effort. Brand advertisers, by definition, do not profit from clicks. When they use CPM bidding, they do not pay by the number of clicks received. Since the click level does not affect their one- period revenues or one-period costs, they are indifferent between high and low effort. Brand advertisers using CPC bids will always minimize effort in a one-period horizon in order to minimize costs. While the one-period incentives are rather straightforward, the dynamic incentives could easily be different. This is where Bayesian Publisher Expectations play a key role. They ensure that the advertiser does not have the ability to profit in future periods by setting a particular costless effort level in period t. Section 6.3 describes, and Appendix C formally shows, that any publisher expectation function that does not exploit past bid type information will be wrong in equilibrium. It is important to note that Bayesian Publisher Expectations do not eliminate brand advertisers’ motivation to avoid clicks. However, they do prevent the advertisers from strategically using this motivation to lower advertising costs. Finally, consider advertisers’ choices of bid types. 37 Lemma 3 Under BPE, direct response advertisers always enter CPM bids. Brand advertisers are always indifferent between the best possible CPM bid and the best possible CPC bid. Lemma 3 indicates that BPE generate a strict preference among direct response advertisers for CPM bids. This comes from the BPE requirement that advertisers “earn” a high click-through expectation. A direct response advertiser is better off if it does not try to earn this high expectation in the first period and, given this decision, it is better off under CPM bidding in all subsequent periods. Brand advertisers are indifferent between optimal CPM bids and optimal CPC bids. It should be noted that Lemmas 1, 2, and 3 do not depend on any stability in other advertisers’ bids. Even if other advertisers are following nonstationary bidding strategies, one can confidently predict the relationship between advertisers’ optimal bid type choices and effort levels. Bayesian Publisher Expectations endogenously limit strategic behavior on the part of brand advertisers by punishing them forever if they ever use CPC bidding. This punishment is effective in that it removes any incentive for brand advertisers to choose CPM bidding over CPC bidding, or vice versa. An unintended consequence of this is its effect on direct response advertisers, who respond by using CPM bidding. However, this unintended consequence does no harm to the affected direct response advertisers. 38 4.3 Equilibrium Existence and Publisher Belief Uniqueness Lemmas 1-3 characterized optimal advertiser behavior under BPE; Proposition 1 now shows that equilibrium exists, and that BPE uniquely maximizes publisher revenues. Proposition 1 At least one equilibrium exists. In any equilibrium, the publisher uses BPE and advertisers behave in accordance with Lemmas 1-3. The advertiser behavior under BPE described in lemmas 1, 2, and 3 satisfy the incentive compatibility and advertiser rationality constraints of Definition 1. Two conditions remain to be proven. The first is that BPE maximizes publisher revenues. The proof of proposition 1 shows that any alternate expectation function either reduces publisher revenues earned from brand advertisers or is inconsistent with the true click-through rate, and no alternate expectation function can increase expenditures paid by direct response advertisers. Second, it is shown that BPE is the only expectation function consistent with advertisers’ equilibrium strategies. It is important to emphasize that BPE uniqueness does not imply equilibrium uniqueness. It is common, in both multi-slot auctions and dynamic games, to have multiplicity of equilibria. Multiplicity arises here due to nonuniqueness of advertisers’ optimal bid levels, and brand advertisers’ bid types. The ability to characterize a unique publisher belief that must hold in any equilibrium of the game indicates the robustness of the paper’s main result. 39 4.4 Comparing the Hybrid Advertising Auction to the Generalized Second Price Auction Many advertising publishers do not currently use hybrid advertising auctions. A natural question is whether auction outcomes in non-hybrid advertising auction mechanisms can be supported by a hybrid advertising auction setting. The answer to this question depends naturally on what other auction mechanism is used. As a baseline, consider the Generalized Second Price (GSP) auction of Edelman et al. (2007). This auction is the one that Google and Yahoo use to allocate advertisers to slots on their search results. The Generalized Second Price auction is the same as the hybrid advertising auction mechanism described in section 4.5 with the exception that it has no CPM bidding option. Proposition 2 Under BPE, any repeated GSP equilibrium assignment of advertisers to slots can also be supported in a repeated hybrid advertising auction. Proposition 2 shows that, under BPE, any GSP equilibrium can be supported by a hybrid advertising auction. When advertisers are offered a CPM bidding option, BPE compels direct response advertisers take it, but doing so leaves publisher revenues unchanged. BPE make brand advertisers indifferent between CPC and CPM bidding, as discussed above. Proposition 2 is somewhat reassuring in that a publisher currently using a GSP auction knows its previous auction outcomes could also be obtained in the hybrid advertising auction setting if it sets the proper expectations. If some advertisers have an unmodeled preference for a CPM bidding option, offering this extra feature could attract advertisers to the publisher’s platform. This possibility is discussed further in section 6.2. 40 5. Alternate Payment Schemes and Social Efficiency This section considers how to increase efficiency within the class of hybrid advertising auction mechanisms. It is well known that the second-price auction (Vickrey 1961, Clarke 1971, Groves 1973 or “VCG”) maximizes social welfare. Three results emerge. First, under a particular restriction of the model, we present a hybrid payment scheme which achieves the socially efficient VCG assignment of advertisers to slots. Second, this proposed payment scheme maximizes publisher revenues among the set of socially optimal payment schemes. Third, in section 5.2, without this restriction of the model, it can be proven that no mechanism always achieves the VCG assignment. 5.1 Efficient Allocation of Advertisers to Slots The basic idea of the VCG mechanism is to charge each advertiser for the externality its purchase imposes on the publisher. As a simple example, imagine a setting with 2 slots and 3 advertisers. Assume advertiser 1 buys the first slot and advertiser 2 buys the second slot. Advertiser 1’s purchase of the first slot reduces the publisher’s revenue from both of the other advertisers relative to a scenario where advertiser 1 does not purchase the first slot. Advertiser 2 is pushed to the second slot, reducing its payment, and advertiser 3 is pushed out of the auction, eliminating its payment. A VCG mechanism corrects for this by charging advertiser 1 according to the publisher’s revenue reduction from each of the other two advertisers. This charge then ensures the lowest-value advertisers do not purchase the highest-value slots. It is well known that the benchmark auction used in the search advertising industry, the Generalized Second Price auction of Edelman et al. (2007), is not guaranteed to reach the socially optimal assignment of advertisers to slots. Similarly, the hybrid advertising auction is 41 not guaranteed to reach the VCG assignment. This follows directly from Proposition 2. Since any GSP equilibrium assignment can be supported in a hybrid advertising auction, and since some GSP equilibrium assignments do not achieve the social optimum, it must be the case that some hybrid advertising auction assignments do not achieve the social optimum. It is therefore interesting to consider how to modify the hybrid advertising auction mechanism to ensure it achieves the socially efficient VCG assignment of advertisers to slots. Part of the analysis in this subsection extends recent work by Aggarwal et al. (2006). Under a restrictive assumption about the model primitives, one can construct a payment scheme that elicits truthful bids and produces the VCG assignment. The assumption needed is that that the position-dependent exposure and click-through rate multipliers fall by the same amount for each slot k. Uniform Value Depletion Condition (UVDC): ,...,K k X X Y Y k k k k 1 , 1 1        . The Uniform Value Depletion Condition is a rather strong restriction on the model. The behavioral implications are as follows. Assume the position-dependent exposure multipliers of the first three slots are 0.5, 0.45, and 0.4, and the position-dependent click-through multiplier of the first slot is 0.2. It must then be the case that the second slot has a click-through multiplier of 0.15 and that the third slot has a click-through multiplier of 0.1. Note, though, that actual click- through rates may still differ because they depend on the ads placed in these slots. The Uniform Value Depletion Condition is useful for two reasons. First, for settings in which it holds, one can establish a socially optimal mechanism. This may be particularly likely 42 when the total number of ad slots K is small. Second, it helps establish the intuition needed to get close to the VCG assignment when the UVDC does not hold. Next, consider how to construct the socially optimal payment scheme under UVDC. There are three challenges in designing this payment scheme to reach the VCG outcome: 1) charging each advertiser for the externality it imposes on the publisher; 2) removing incentives for advertisers to misreport their valuations (truthful bidding); and 3) (conditional on achieving the VCG outcome) maximizing publisher revenues. Definition 2 gives the prices that accomplish this. For notational convenience, let ) ( c g I kt  be an indicator function that equals one when the advertiser in slot k in period t enters a CPC bid, and let ) ( m g I kt  be an indicator function that equals one when the advertiser in slot k in period t enters a CPM bid. Definition 3 For K k   1 , define it g ikt p as i’s payment for slot k in period t given bid type it g . c ikt p is a per-click payment charged when i enters a CPC bid while m ikt p is per- exposure payment charged when i enters a CPM bid. For K k ,..., 1  let                                           . if ) ( ) ( ) ( ) ( if ) ( ) ( ) ( ) ( ' ' 1 ' 1 ' 1 ' ' 1 ' 1 ' 1 ' 1 ' ' ' ' 1 ' 1 ' 1 ' ' 1 ' 1 ' 1 ' 1 ' ' K k k K k k it t k m t k k k t k k c t k E t k k k k K k k K k k it t k k E it m t k k k k k t k c t k E it E t k k k k g ikt m g m g I b X X c g I Y b X X X c g m g I X b Y X X X c g I b X X X p it     When an advertiser gets a slot in the hybrid auction, it pushes all lower bidders to lower slots. When these bidders are allocated to lower slots, they pay for fewer clicks and impressions thereby reducing the amount of money the publisher receives from those advertisers. The 43 payment scheme in Definition 3 essentially forces the advertiser in slot k to compensate the publisher for the revenue lost from all lower advertisers. Proposition 3 establishes that the proposed payment scheme achieves the VCG assignment. Equilibrium truth-telling requires that each direct response advertiser i in each slot k will bid Di c it r b  or Di it m it r b   and that each brand advertiser i in each slot k will bid it Bi c it r b   or Bi m it r b  . Notice that, as in a second-price auction, the payment of the advertiser in slot k is not a function of that advertiser’s own bid. Proposition 3 Under the Uniform Value Depletion Condition, the payment scheme in Definition 3 produces a unique equilibrium with truthful advertiser bids and the VCG allocation of advertisers to slots. Proposition 3 shows that truthful bidding is a strictly dominant strategy under the payment scheme proposed in Definition 3. This is proven by considering an advertiser with the k th highest expected payment. This advertiser will strictly prefer slot 1 '  k to slot k' for any slot k k  ' . The same advertiser will also strictly prefer 1 '  k to slot k' for any slot k k  ' . Applied recursively and to all slots and all advertisers, it can be seen that the proposed payment scheme will always allocate each advertiser to its socially efficient place in the ad ranking. Proposition 4 Under the Uniform Value Depletion Condition, no other truth-telling payment scheme produces higher revenues. 44 Proposition 4 establishes that the proposed payment scheme maximizes publisher revenues among the class of payment schemes that achieve the VCG assignment of advertisers to slots. Interestingly, Propositions 3 and 4 do not rely on any assumptions about publisher expectations. Direct response advertisers always exert high effort, independent of publisher expectations. This is because Definition 3 ensures that they are charged less than their valuation, and therefore additional clicks always increase profits. Brand advertisers are indifferent between high effort and low effort. Proposition B1 in Appendix B formalizes these results. A relatively minor operational concern in implementing this mechanism is that, while there have been assumed K slots throughout, Definition 3 requires values for 1  K X and 1  K Y . There are various ways to handle this. Perhaps the most natural would be to experiment with adding an additional advertising slot K+1, measuring 1  K X and 1  K Y for this slot, and then using these figures in the calculation of it g ikt p . It also may be possible to endogenize K. 5.2 Nonexistence of Efficient Mechanisms without the UVDC When the Uniform Value Depletion Condition holds, one is able to construct a payment scheme that achieves the socially optimal assignment of advertisers to slots. But when this condition does not hold, there is no payment scheme that can reliably achieve this assignment in equilibrium. Proposition 5 If the Uniform Value Depletion Condition fails to hold for some slot k, no payment scheme will always achieve the VCG assignment of advertisers to slots. 45 Proposition 5 is a non-existence result. When UVDC does not hold, there is no payment scheme that always achieves the VCG assignment. Recall that the core principle of the VCG equilibrium is to charge each advertiser for the harm that its inclusion does to the publisher. When UVDC does not hold, the reduction in publisher revenues from moving advertiser i from slot k to slot 1  k depends on advertiser i’s type since exposure rate multipliers and click- through rate multipliers decrease nonuniformly. Since advertiser types are private, the publisher cannot know its revenue loss from each advertiser and therefore cannot charge i for the externality generated by its inclusion. While there is no socially optimal payment scheme without UVDC, it may be possible for the publisher to design a payment scheme that gets “close” to the VCG assignment. There are two key criteria to consider. First is the mix of advertiser types in the population of advertisers. For example, if 99% of revenues come from brand advertisers, then advertiser externalities are more likely to depend on the differences in exposure multipliers than the differences in click- through multipliers and Definition 3 can be modified appropriately. The second criterion is the rates at which exposure and click-through multipliers decrease across slots. For example, it could be argued that k X Y k k   , since an ad exposure is necessary but not sufficient for a click (in the absence of random clicking). If this is the case, and if UVDC does not hold, then it seems intuitive to expect that 1 1      k k k k X X Y Y . Therefore, the harm done in moving a brand advertiser one slot lower in the ranking is likely to exceed the harm in moving a direct response advertiser one slot lower in the ranking. This difference in externality sizes across advertiser types could also be used to modify the payment scheme in Definition 3 in an attempt to get “close” to the VCG assignment. 46 6. Discussion and Implications This paper has presented the first analysis of equilibrium in a hybrid advertising auction. It has shown that the publisher’s expectations play a key role in whether offering multiple bid types will reduce seller revenues. The analysis has produced several results that could influence publishers’, advertisers’, and policymakers’ actions. These implications are especially relevant to publishers that do not currently offer hybrid auctions, but may do so in the future. 6.1 Conventional Wisdom in Hybrid Advertising Auctions CPM ad pricing has traditionally been associated with brand advertisers. CPM pricing has been the standard ad price metric in traditional advertising media (e.g., television, newspapers, billboards) for decades. These media were typically dominated by brand advertisers, leading to the association. CPM pricing continues to be standard in online display advertising (Evans 2008). CPC pricing, by contrast, is relatively new. It was invented by GoTo.com in 1998 in a successful effort to lure advertisers from rival websites. Google used CPM pricing before adopting the quality-weighted CPC model in 2002 in order to prevent advertisers from purchasing prominent search ad positions with low-click ads (Battelle 2005). 5 Early search advertising was dominated by direct response advertisers. Since these advertisers can usually track consumer profitability at a fine level of granularity, CPC pricing allows them to compare their marginal profits and advertising cost at the level of the individual click. Direct response advertisers prefer CPC pricing and tend to be associated with its use. 5 We thank a reviewer for pointing this out. 47 Facebook’s help file, shown in Figure 5, explains the industry’s conventional wisdom: “As a CPC advertiser you are indicating that what is most important to you is having people click through to your website and controlling the actual cost to drive each individual person to your site. As a CPM advertiser you are indicating that it is more important to you that many people see your ad, not that they actually take action after seeing your ad. CPM advertising is usually more effective for advertisers who want to raise awareness of their brand or company, while CPC advertising is more effective for advertisers who are hoping for a certain response from users (like sales or registrations).” It appears that many advertisers believe this conventional wisdom. For example, Newcomb (2005) quotes an advertising executive saying “if the search campaign is largely for branding purposes, we will migrate to the CPM pricing model and bid as high as we can afford. For direct response clients, we’ll stick to CPC…” An extensive search produced no statements contradicting the conventional wisdom at the time the first draft of this paper was written. However, since then, some practitioners seem to have understood the conventional wisdom was flawed; see, e.g., Keane (2010). Lemmas 1-3 and Proposition 1 show that this conventional wisdom is inconsistent with equilibrium publisher beliefs. These results may suggest that advertisers should think carefully about their optimal choice of bid types conditional on optimal publisher expectations. When advertisers face a rational publisher, Bayesian Publisher Expectations, direct response advertisers should always use CPM bidding. If advertisers purchase slots from a publisher that does not understand the analysis in this paper, it will likely be the case that direct response advertisers 48 face lower costs under CPM bids with high costless effort, and brand advertisers will be more profitable using CPC bids with low costless effort. If an advertiser does not know the publisher’s expectation function, it would be advisable to test an identical set of ads under two different campaigns, one using CPC bidding and the other using CPM bidding, to see which performs better. 6.2 Should Publishers Offer Hybrid Advertising Auctions? Proposition 2 shows that any equilibrium outcome in a Generalized Second Price auction format can also be supported in a hybrid advertising auction. Equilibrium advertiser behavior guaranteed by Lemmas 1-3 and BPE suggest that offering multiple bid types might not reduce revenue relative to a pure CPC auction. However, this implication is subject to the caveat that it assumes perfectly rational advertisers, since this model does not have a unique equilibrium. While we do not see a reason that offering multiple bid types would lead advertisers to change their equilibrium strategies, it is impossible to rule the possibility out. Publishers may have an additional, unmodeled incentive to offer multiple types of bid. As mentioned above, CPM ad pricing has been traditionally associated with brand advertisers while CPC ad pricing was developed for direct response advertisers. It may be that these advertisers are less than fully rational, or that they have some cost of adopting a non-preferred ad price metric; if so, then offering multiple bid types may attract some set of advertisers to a publisher’s platform. For example, CPM bidding may facilitate price comparisons across advertising media. Offering multiple bid types could increase publisher revenues since auction prices depend critically on the degree of competition in the auction. This platform adoption argument suggests that publishers may find it worthwhile to experiment with offering multiple types of bid. 49 At the time of writing, the online advertising market still appeared to be converging to equilibrium. If advertisers become accustomed to having multiple bidding options, they may demand them from other websites. Since the hybrid auction has been adopted by the advertising sales leader (Google) and internet traffic leader (Facebook), one might speculate that more companies will adopt it in the future. One barrier to adopting the hybrid auction may be the associated complexity in forming click-through expectations; a major purpose for the present analysis is to show that offering multiple bid types need not harm auction efficiency or publisher revenues. Since multiple bid options may offer advertisers some benefit of convenience, and has no apparent downside for publishers, it seems natural to speculate that more companies will adopt it in the future. We would predict adoption would be most likely by those publishers whose advertising inventory appeals to both brand advertisers and direct response advertisers. 6.3 Historical Publisher Expectations This paper has heretofore considered a strategic publisher that sets click-through expectations to maximize its profits. This requires that the publisher disbelieve the conventional wisdom described in Section 6.1. However, Facebook’s statement in Figure 5 reinforces this conventional wisdom. In addition, Bayesian Publisher Expectations requires use of an advertiser’s bid type in addition to its past click-through rates. Figure 4 makes it clear that Google’s quality scores are not based on past bid types. This evidence suggests that publishers currently offering hybrid auctions may not set fully rational click-through expectations. In addition, publishers that might offer hybrid auctions in the future may not have a full appreciation for the intricacies of this auction format. 50 This section considers what may happen if the publisher is not fully rational. A natural way for a nonstrategic publisher to set click-through expectations would be to look at each advertiser’s past click-through performance, as suggested by Google’s statements in Figure 4. We call this “Historical Publisher Expectations” or HPE. Appendix C proves a series of results based on a publisher expectation function that only considers past click-through rates. This section discusses the intuition for these results and what they imply for publishers. First, we formalize the idea (mentioned above) of a “bid reversal” as a multi-step process in which a brand advertiser first enters a series of CPM bids with high effort levels. Because the CPM bid option is used, the high effort does not increase the advertiser’s cost, but it does increase the publisher’s expectation of future click-through rates. In the final step, the advertiser can enter a CPC bid with a low effort level. Under HPE, this series of actions may lower its costs. A repeated bid reversal is called a “Lattice Strategy.” Two main results emerge. First, when the publisher uses HPE, every brand advertiser will engage in at least one bid reversal during the course of the game. Second, when the publisher uses HPE, there are regions of parameter space in which brand advertisers will use bid reversals with very high frequencies. This second result is proven by employing the One-Stage Deviation Principle of Blackwell (1965) to show that a two-period bid reversal strategy may be played repeatedly in equilibrium. A clear implication of the model is its prediction that publishers should use past periods’ bid types as an additional factor in setting click through rate expectations. It is necessary to consider that if a bidder switches bid type several times, it may be following a Lattice Strategy and the publisher should lower its click-through rate expectations appropriately. Understanding 51 this insight is particularly important for sellers that do not currently offer hybrid advertising auctions to maximize hybrid auction revenues. An alternate mechanism to prevent the use of the Lattice Strategy is to “reset” click- through expectations to zero for any new advertisement, even when it is a minor variation on an old ad, as Google does. (Facebook does not currently disclose its policy.) The downside to this strategy is that a low-click advertiser can repeatedly formulate new advertisements, and each new low-click ad will be given a “blank slate” and placed appropriately. Instead, it may be more profitable to borrow information across many similar ads to set click-through expectations and incorporate data on past bidding behavior, as required by Bayesian Publisher Expectations. 6.4 Public Policy Implications It is conceivable that search engines could be subject to enhanced regulatory attention in the future. Google dominates the US market, with 66% of all clicks. Calculated using shares of total clicks, the industry has a Herfindahl Index of 0.47 (Munarriz 2010). This is well above the 0.18 threshold at which the US Justice Department considers a market “concentrated” and subject to enhanced merger scrutiny. This dominance is even more pronounced in other countries. For example, Google’s share of clicks exceeds 90% in Germany and France. If policymakers regulate publishers’ business models in the future, it may be relevant to ask what type of auction enhances social welfare. This paper has shown how to achieve the social optimum exactly when the Uniform Value Depletion Condition holds. It has also shown that without this condition no payment scheme will always achieve the social optimum in a hybrid auction setting. But the discussion in section 5.2 reveals how to get close to the socially 52 optimal payment scheme, taking into account advertiser heterogeneity and the rates at which clickthrough and exposure multipliers decrease across ad slots. These results may interest search engines even in the absence of regulatory attention. If advertisers’ values per click and impression are correlated with viewers’ utility of seeing advertisers’ ads, implementing a payment scheme to get close to the social optimum would likely improve consumers’ utility of the search platform. This may help a search engine attract eyeballs which it can then monetize through additional ad sales. 6.5 Maximizing Publisher Auction Revenues An important and interesting question not broached here is how to design a hybrid auction mechanism to maximize publisher revenues, without regard for the social optimum. This is difficult in the current setting because advertisers are heterogeneous in two dimensions: type and reservation value. The starting point for this topic is the seminal work of Myerson (1981). For analytical tractability, Myerson (1981) assumed that bidders’ values were drawn from a single distribution function and derived a symmetric equilibrium. Ulku (2009) extended Myerson’s framework to allow bidders to have one-dimensional private information and showed how to find an optimal auction mechanism with a “generalized” virtual value. Edelman and Schwarz (2010) applied this framework in the GSP under an assumption that advertisers only differ in one dimension: value per click. If the valuations of both brand advertisers and direct response advertisers can be collapsed into a single index of advertiser differentiation, their framework could be applied to hybrid auctions. To the best of our knowledge, optimal mechanism design when selling 53 heterogeneous objects to bidders that differ in more than one dimension is an extremely difficult and unsolved problem; this, then, is a profitable direction for future research. 54 CHAPTER TWO: THE SELECTIVE REPORTING OF FACUAL CONTENT BY COMMERCIAL MEDIA 1. Introduction Consumers demand useful information to improve their understanding of the world and make better choices in their lives. This information, referred to hereinafter as factual content, is typically provided by commercial media, who earn profit by collecting payments (money or attention) from readers or advertisers. In this paper, we study the marketing of factual content by such media and examine how the market structure of the commercial media industry affects medias’ content strategies. The internet and mobile technology have made it easier and cheaper to distribute factual content. Newspapers, magazines, radio stations, and television, distribute factual content through the internet and mobile devices. In addition, there are thousands of online-only distributors of content as well (e.g. slate.com), not to mention the countless number of bloggers who provide factual content for commercial gain. The emergence of these technologies has, consequently, increased competition for readers’ attention. The central question we ask in this research is whether this increase in competition corresponds to an increase in the provision of factual content? The answer to this question is not obvious because factual content is not a standard product. A special feature of factual content is that it is made up of two components: the facts themselves and the overall picture told by the collection of presented facts. Facts themselves are objective and, while novel and interesting in their own right, they do not provide a comprehensive sense of the state of the world (or simply the state). Viewed collectively, however, facts offer such a perspective. And, the more facts one is presented about a certain 55 issue, the better her perspective becomes and the closer she is to having an accurate understanding of the true state of the world. For many important issues, we rely on commercial media to present a collection of facts of their choosing. And, because of consumers’ common desire to learn the true state, media have an incentive to provide a credible perspective supported by a lot of factual evidence. Confounding this incentive, however, is that people prefer that the perspective offered by the collection of facts be consistent with their opinions, all else equal <cite psychology and communications literature – see MS for a possible list of papers>. And, since consumers hold varied opinions on most issues, a commercial medium is forced to balance consumers’ desire for credibility with their preference for content that matches their opinion. This trade-off, the fundamental aspect of our research, implies that media must selectively omit some facts so that the overall collection of presented facts fits the desired perspective – a notion we call media slant. In contrast to previous work on media slant, our study focuses on the micro-foundations of how slant is constructed via the careful selection of objective facts. To illustrate the selection process in practice, consider the issue of global warming, which was among the top 10 subjects of interest among Americans during the period 1986–2006 (Robinson 2007). The media report the subject differently. For example, a New York Times report had the title “Past Decade Warmest on Record, NASA Data Shows”, 6 and it contained the following two scientific facts: (1) “2009 was the second warmest year since 1880, when modern temperature measurement began,” and (2) “An upward temperature trend of about 0.36 degrees Fahrenheit (0.2 degrees Celsius) per decade over the past 30 years.” In contrast, the Wall Street Journal reported an article with the title: “Global Warming Models Are Wrong Again.” 7 In this article, they referred to two facts: (1) 6 http://www.nytimes.com/2010/01/22/science/earth/22warming.html. Accessed May 2012. 7 http://online.wsj.com/article/SB10001424052702304636404577291352882984274.html. Accessed May 2012. 56 “(February 2012) monthly global temperature …was minus 0.12 degrees Celsius, slightly less than the average since …1979,” and (2) “Weather conditions similar to 2012 occurred in the winter of 1942.” The cited sentences from New York Times and Wall Street Journal are separate facts generated from the same state of the world. As we can see, the first two give readers the impression that global warming is occurring, but the last two provoke consumers’ skepticism about its occurrence. Furthermore, the New York Times report does not mention any facts that support global warming skepticism and the Wall Street Journal report does not mention any facts that support global warming. It suggests that the facts embedded in these reports were carefully chosen so that they support the respective stances as indicated in the titles of the reports. 8 Arguably, the idea that media may slant their reports is suspected by most consumers. Popular political commentators (Coulter, 2002 and Franken, 2003) as well as academics (Groseclose & Milyo 2005, and Gentzkow & Shapiro 2011) have written about the US media’s attempt to appeal to consumers’ opinion though the slanting of reports. Anticipation of a medium’s incentive to slant its content implies that a consumer can infer something about the quality of the reporting (the number of facts) by observing the media’s stance on an issue. For example, even before reading the body of the reports mentioned above, readers can anticipate that few facts of global warming skepticism will be presented in the first report and that little content supporting global warming’s occurrence will be found in the second one. Therefore, the media stance indicates the type and quality of information consumers expect before they decide which medium to read. If consumers update their beliefs based on their observations of media stances, even if slanted, they can improve their understanding about the state of the world. This is a key departure from earlier work on media slant (MS & XS), which assumes consumers have 8 An alternative interpretation is that these media possess more facts than they can possibly report due space or bandwidth constraints. We consider settings in which such constraints are not binding. For instance, NYT and WSJ have reported repeatedly on important topics like global warming and maintained similar stances over time. 57 no ability to learn something other than what they are explicitly told by the media. This distinction forms a key novelty of this research. Furthermore, by endowing consumers with the ability to anticipate the incentives for slant implies that strategic media must account for consumer’s anticipation of slant when choosing what content to report. By including this additional consideration, we provoke extant intuitions about media bias, polarization, and journalistic balance. We compare various media market structures and assess the degree to which consumers can meaningfully update beliefs about the state of the world from the available media options, a measure which we call “media informativeness”. To illustrate this measure consider two scenarios. First, suppose the New York Times is the only medium to report on global warming. After knowing the stance, consumers update their beliefs (possibly imperfectly) in favor of global warming’s occurrence. However, when both New York Times and Wall Street Journal cover the same subject matter, consumers are unable to update their beliefs since their stances are opposing. In this example, media informativeness is higher in the first scenario in which there is only one medium. The idea that media can slant their content by taking a stance different than how they actually observe the state of the world gives rise to the notion of media bias. It is commonly believed that stronger bias in the media is associated with consumers being less informed. However, in our setting consumers understand the incentive for biased reporting and may, therefore, infer something about the state of the world from media stances, even if slanted. This raises the question of whether media bias is a good measure of consumer ignorance. We find, in fact, that more informative reporting is not necessarily associated with less media bias. 58 We highlight the three most important findings from this research. The first regards the impact of competition on the content provision of media. We find that competition does not increase media content provision, and, when the value consumers place on facts is large, competition strictly reduces it. Under monopoly, despite consumers’ like-minded preferences for additional facts and accurate reporting, if consumers value (even mildly) content that matches their opinions, the medium does not provide all the facts. However, if consumers’ desire for factual content is high enough, the medium provides partially informative reports with more facts. The media stance in this situation serves as a signal, which can help consumers update their knowledge about the state of the world. When consumers observe the media stance, they believe the actual state of the world is in the neighborhood of the chosen stance. Therefore, they have higher expectations about the quality of the report – the amount of supporting facts it contains. With competition, however, we find that duopolistic media produce uninformative content with lower quality reports that contain fewer facts than under monopoly. The pressure of competition drives the media to purposely choose a stance, which jams the opposing view by providing conflicting statements about the state of the world. It is important to note that opposing media stances are not simply product differentiation strategies. Rather, a medium chooses an opposing stance in order to disable consumers’ ability to determine which medium is more informative and eliminate its rival’s potential competitive advantage in content quality. Hence, no medium can be informative in equilibrium, and as a result we find that each medium produces content with fewer facts. This outcome, in fact, may be connected to the growth of micro-blogging platforms such as Facebook, Twitter and Tumblr in reaction to the intensified competition of internet content, in order to conceal the reduction of facts provision. 59 Our second result regards the impact of competition on polarization and media extremism. In contrast to earlier work on media slant (Mullainathan & Shleifer 2005, hereinafter MS; and Xiang & Sarvary 2007, hereinafter XS), we find that a monopoly medium may take more extreme positions than duopolistic media. Stances in a duopoly are independent of the state of the world because their stances are motivated by the desire to confuse consumers about which medium has more facts. As noted above, they do this by choosing opposite stances rather than by maximally differentiating their product (MS, XS). The rival takes a mirror (though not necessary extreme) stance to eradicate the informative medium’s competitive advantage and thereby focus readers’ choices solely on their opinions. Even though competitive media may take conflicting positions, they do so only to the extent of heterogeneity in consumer opinion. If consumers’ opinions are relatively consensual, the competitive media need not choose extreme stances to prevent consumers from updating their beliefs. The monopolist, on the other hand, may want to take an extreme stance to communicate that its report is of high quality in that it contains a lot of facts. Finally, our third finding challenges the use of media bias as a measure of consumers’ ability to be informed. The term “media bias” has been well discussed in the literature and is typically defined as the expected relative difference between the media report and the underlying state. We find that media bias is an imperfect indicator of the quality of communication between media and consumers. More specifically, more-informative reporting does not necessarily equate to lower media bias. If consumers sufficiently value facts, a monopoly medium will slant its report toward a more extreme position in order to increase consumers’ expectation about the quality of its report. In this way, more-informative reporting does not necessarily correspond to less media bias. Additionally, because competition (weakly) reduces media informativeness, we 60 find that competition may actually shrink media bias. This result is sharply different from previous findings in most papers that competition (weakly) increases media bias. This paper relates to the literature on media strategies and the influence of commercial incentives on content provision. Gal-Or and Dukes (2003) and Anderson and Coate (2005), Godes et al. (2009) among others, consider media strategies in which the content is non- informational (e.g., entertainment). In the current paper, we focus on media strategies when the content is factual and when consumers desire objective information. While more recent work has explored media competition in markets for informational products, their focus has been on identifying factors leading to media bias. Most notably, MS, Anand et al. (2007), and XS identify the incentives of duopolists to slant news to extreme positions in order to differentiate their content from that of competitors, which results in greater media bias in news reporting. Ellman and Germano (2009), Gal-Or et al. (2012), and Yildirim et al. (2011) explore the relationship between the media’s desire to appeal to advertisers’ interests and media bias. Our focus, in contrast, is on how media choose to present or conceal factual content and the extent to which consumers become informed. Also, unlike the previously mentioned research, we focus on consumers’ desire for objective facts and their ability to infer information from the media’s marketing strategies. This distinction is important for two reasons. First, if consumers have a common desire for content with more factual support, then media create value for customers by being more informative. With this consideration, it is not entirely clear whether commercial incentives or competition will exacerbate or mitigate media bias. Second, if consumers are able to anticipate incentives for biased content, consumers may be able to make inferences from media strategies and update their understanding about the state of the world. Consequently, our work introduces 61 the notion that media bias may not be the best measure of reader ignorance. This is a relevant distinction in light of the attention shown to identifying and empirically measuring media bias in the news media (Lichter et al. 1986, Groseclose & Milyo 2005, and Gentzkow & Shapiro 2010). Similar to our work, Strö mberg (2004), Anand et al. (2007), and XS study the incentives of media to provide objective factual content. Strö mberg (2004) focuses on information that is related to popular elections, and Anand et al. (2007) are concerned with the verifiability of facts. XS introduce the notion of the conscientious consumer who has no personal opinions. Despite having “unbiased” consumers, XS show that extreme positions arise in equilibrium. The micro- foundation in our work is closest to XS, with three important distinctions. First, we concentrate on the notion that consumers enjoy reading factual content, and therefore more facts are better for consumers. Second, we permit consumers to make inferences based on the stances media take. Because consumers make such inferences, they are can be informed about the state of the world despite media slanting. Third, while XS assume that the media’s ability to slant their reporting is bounded, we assume that the media can always generate a report to support the stance. From the media’s perspective, if facts are assumed to be truthful, then a stance binds them to reporting a set of facts that are consistent with that stance. It is not entirely clear how these forces affect the incentives for media slant as a differentiation strategy, as found in earlier work. We consider a setting in which the media declare their stances publically so that they are known to consumers before they read or purchase a report. Such is the case when consumers can read headlines before choosing which medium to consume or when media declare their general positioning. It is through this declaration that consumers may update their beliefs about the state of the world and estimate the number of facts a medium will provide in its report. In this sense, 62 stances resemble “cheap-talk” (Crawford & Sobel 1982, hereinafter CS). 9 As in CS, our setting exhibits a “less-than-fully informative” equilibrium in which the support of the information variable is partitioned in a countable set of intervals and the sender (the medium) reports a message (a stance) only when the observed information lies in the associated interval. But, in contrast to the cheap-talk literature, the sender’s message serves two roles. In addition to serving as a signaling mechanism to (partially) inform consumers about the state of the world, the message also serves a positioning function, in which the stance enters consumers’ utility, through appeals to their opinions. These two features imply that the communication process between the information sender (media) and the receiver (consumers) in our framework is a non-trivial extension of a cheap-talk game. Nevertheless, the cheap-talk approach is helpful in understanding how commercial incentives confound the media’s ability to be fully informative and why the informativeness of media reporting and content provision are affected by competition. 2. The Model In this section, we first discuss the fundamental connection between the state of the world and the generation of facts. We then illustrate how the choice of stance binds the medium’s maximum number of facts in the report, and then derive consumers’ demands for both the media’s reports. For consistency, we use the term media to represent the commercial information providers, websites, news outlets, and UGC platforms, which observe and (selectively) report factual content in exchange for a payoff. The term report refers to the mixture of facts that the 9 While our monopoly model involves a single sender (as in CS), the duopoly media model we analyze has multiple senders. Cheap-talk with multiple senders has been studied in a variety of settings (Gilligan & Krehbiel 1989, Krishna & Morgan 2001) and more generally in Battaglini (2002). This earlier work takes the receivers’ preferences among senders as exogenous. In our duopolistic media setting, however, we assume consumers’ preferences for senders is determined endogenously by the senders’ choice of stance. 63 media choose to present to support their stance. The term consumer represents the readers or viewers. 2.1 The State of the World and the Source of Facts The state of the world, or simply the state, represents the underlying truth about some focal event or subject. We assume that the state is a random variable, t, that is uniformly distributed between ] 1 , 0 [ . Relating to the opening example, a value of 0.4  t means that there is a 40% chance that global warming is occurring. The value of the state t dictates the overall composition of the set of facts. Each fact has incremental value to consumers in the form of novel information. In addition, each fact contains a binary signal } 1 , 0 {  Y about t. In the global- warming example, “2009 was the second warmest year since 1880,” and (2) “An upward temperature trend of about 0.36 degrees Fahrenheit … per decade over the past 30 years” are two facts that contain different informational content but that are both associated with an affirmative signal, 1  Y , or that global warming is occurring. However, “Weather conditions similar to 2012 occurred in the winter of 1942” is an alternative fact, that contains an opposite signal, 0  Y , about the occurrence of global warming. We further assume that every signal, Y , is an independently and identically distributed (i.i.d.) random draw from a Bernoulli process with t Y   ) 1 Pr( , and t Y    1 ) 0 Pr( . 10 Let  denote the total number of available facts, and assume that every medium observes all of the facts. Let  denote the total number of observable facts, and assume that 10 The fact-generation process in previous literature (Hayakawa 1990, MS, XS) assumes that the facts are only a string of data consisting of 0s and 1s. In our setting, there is additional value from facts – each contains a novel piece of information that readers consume. We specify this in more detail section 2.3. 64 every medium observes all of the facts. 11 Among them, 0  we have facts with signal 0 and 1  facts with signal 1, and      1 0 . 2.2 Media Stances and Reports Each medium chooses a stance s, which represents an announcement about the state of the world. A stance is supported by a report – a combination of facts that serve as evidence for the chosen stance. We assume that the media can only report “true” facts and cannot fabricate non-existing facts. Therefore, the maximum number of facts in a report can never exceed total amount facts  . We also require media reports to be consistent with the chosen stance. This requirement implies that if a medium’s stance affects the number of facts it can report. To illustrate this key implication, let   n be the number of reported facts and n n n  1 0 , be the number of facts with signal 0 and 1, respectively. By announcing s, the total number of facts must satisfy n n s 1  . The consistency between stance and reports therefore implies the following inequalities: 0 0 ) 1 (      s n n and 1 1     s n n . Hence, the total number of observable facts and the choice of media stance s bounds the maximum number of facts in a report. Because a stance is more credible the more factual evidence used to support it, consumers always prefer more facts to less. So we can restrict attention to maximum number of facts n a medium can report for a given stance s. We can see that 11 This is an important assumption for this model. A considerable amount of the previous literature has made the same assumption. For example: MS, XS and Gal-or et al. (2012). This assumption allows us to abstract away the fact collection process and focus on the selective reporting problem. Note it is possible to think about an asymmetry model that media have different investigation and acquisition cost. We find, however, only a sufficient level of such asymmetry can overturn the main results of this paper. 65 s n    1 0 , if and only if t s  , and otherwise s n 1   or } , min{ 1 0 1 s s n     . In order to avoid the rounding problem, we also assume that n is continuous. To help the reader to better understand the trade-off between the media stance and the number of facts, we use a simple numerical example to illustrate the idea. Table 2. A Numerical Example Facts: Content A B C D E F G H I J Facts: Signals 0 1 0 0 1 1 0 1 0 0 Table 2 shows a case in which 10   and 0.4  t . As we can see, among a total of 10 facts, the facts A, C, D, G, I, and J contain signal 0, and facts B, E, F, and H contain signal 1. Now, suppose that the medium chooses to produce a report with media stance 5 . 0  s . To support this stance, factual content must satisfy n n n s 0   , or simply 1 0 n n  . However, there are 6 facts with signal 0 but only 4 facts with signal 1 in the total data set. The best the medium can do is to produce a report with all 4 facts with signal 1 and randomly pick another 4 facts with signal 0 to fulfill the media stance 5 . 0  s . In this situation, n is 8. Now, suppose that the medium wants to produce a report with media stance 8 . 0  s . We can clearly see this media report has been slanted farther away from the state of the world, 0.4  t . To support this media stance, we need 4 0 1  n n , or for every fact with signal 0 we need 4 facts with signal 1. Because we only have 4 facts (B, E, F, and H) that contain signal 1, the best the medium can do is to combine these 4 facts with a fact of signal 0. Therefore, n is 5 under the second stance, which is fewer than the maximum number of facts the medium can report when 5 . 0  s . As these examples demonstrate, the further a medium’s stance is from the state, the fewer facts it can use in its report to support that stance. 66 2.3 Consumer Demand We model the consumer’s utility function in the following manner. Recall that each fact not only represents a signal, 0 or 1, but also contains unique novel information and a piece of supporting evidence for a chosen stance. Consumers obtain positive utility from reading an additional fact in a report because it provides a more convincing support of the stance. Therefore, more facts always increase a consumer’s willingness-to-pay for the report. This preference structure embeds consumers’ inherent desire to learn the true state of the world. Consumers also have opinions and, all else equal, prefer reports to be consistent with their opinions. Thus, we assume consumers will pay more for a report when the media stance is close to the consumers’ opinions. Denote a consumer by her opinion, b, in [z,1– z], where 2 1 0   z . We assume ] 1 , [ ~ z z U b  , where z captures the divergence of the consumer opinion space. 12 A higher z means that consumers are more homogenous about the state, and a lower z means that the opinion is more diversified. Consumer b’s expected utility function from reading the report on media outlet A is given by:     ] | ) ( [ | , , 2 s p b s d Mn V E s p s n u E b      , (1) where V is the intrinsic value of consuming the report, and M and d represent the consumer’s preference about the number of facts and about reading a report that differs from her opinion, respectively. Hence, M and d are assumed to be non-negative. 13 12 The scope of consumer opinion when z > 0 is smaller than the scope for the state of the world. This permits the possibility of states that exceed relatively narrow opinion (e.g. 14 th Century opinions that the world was flat.) Media also have the additional flexibility to take stances even more extreme than consumer opinion to signal that their stances are supported with many facts. Restricting z = 0 aligns the set of consumer opinion with the state of the world, but does not alter the basic findings. 13 A simplification embedded in (1) is that every fact has equal value to consumers. While in reality different facts might have different effects on consumer preferences, this assumption simplifies our analysis by assuming that consumers have linear marginal utility from reading extra facts. However, our results hold as long as consumers’ valuation for facts is increasing and weakly concave. 67 Even though consumers observe a medium’s stance, s, before deciding whether to buy the report, they do not know exactly how many facts the report will contain. Consumers must, therefore, formalize their beliefs about the state of the world based on the medium’s stance in order to formalize an expectation about the number of facts and make a purchase decision. The consumer’s prior belief about the state is ] 1 , 0 [ ~ U t , and therefore the updated belief   s t |  , is also a distribution on t. Consumers also observe a medium’s pricing decision before deciding whether to purchase, so a natural question to ask is whether consumers can utilize p to update their beliefs about the state t. Even though we make no restriction on consumer’s ability to do so, it is impossible for price to ever serve as a signal in our model. A necessary condition for a separating equilibrium involving prices is the “single-crossing property” of firm types’ profit functions. This condition is absent in our model because all firm types (as defined by the expected number of facts in their report) have the same full-information optimal price. 14 Therefore, the only firm decision, which may possibly facilitate updated beliefs about t is the medium’s stance. A consumer receives zero utility if she does not read any report and will purchase the report as long as it gives them non-negative utility. We also assume that V is large enough so that it is always optimal for the media to serve all consumers. If the media stance reflects the true state of the world consumers believe it, then a consumer’s utility from consuming the report is   p b s d M V p s n u b       2 ) ( , , . However, as we will show in the next section, such an outcome is impossible in equilibrium as long as consumers value reports consistent with their opinion, 0  d . 14 Additional details of this argument are provided in a supplemental appendix available from the authors. 68 In order to derive equilibria in this game, we treat media stances as a form of “cheap talk” (CS). As in cheap talk settings, the only feasible pure-strategy equilibria take the form of an interval equilibrium. An interval equilibrium is characterized by a partition x i i a 0 } {  , some integer 0  x , with 1 0 0     x a a  in which the media stance is ] , [ 1 i i i a a s   , for any ] , [ 1 i i a a t   , where i represents the index of interval. Under this situation, the number of facts that the medium will produce is                     otherwise ; 1 ) 1 ( 1 t if 0 1 s t s s s t s n i . (2) Therefore, the expected utility under this situation is             . ) ( ] ) 1 ( 2 ) 1 ( 2 2 1 [ ) ( ) ( ] ) ( 1 1 ) ( [ 1 ) Pr( | , , ) Pr( | , , | , , 2 2 2 1 1 2 1 1 1 1 1 p b s d s a s a a a M V p b s d dt t f s t dt t f s t M a a V a t s a t s p s n u E s t a s t a p s n u E a s a p s n u E i i i i i i i i s a a s i i i i i i i i i b i i i i i b i i i i b i i i i                                           (3) Given the belief that ] , [ 1 i i a a t   , the consumer with opinion b will purchase a report if and only if     0 | , ,  i i b s p s n u E . (4) Because  M always appear together, we normalize 1   without loss of generality. In this paper, we consider the case that consumers’ opinions are not influenced by the updated belief. In other words, the consumers’ opinions are made up but they still value the reports with more facts. 2.4 Game Timing The timing of the game is as follows. 69 Step 1: The media outlet observes all available facts, announces a stance, s , and generates a report. If there are two media outlets, they announce their stances simultaneously. Step 2: The media outlet announces the price, p, for its report. If there are two media outlets, they announce their prices simultaneously. Step 3: Consumers update their beliefs about the state of the world, t, formalize their expectations about the reading utility associated with the media based on the media stance and the price, and then make their purchasing decisions. Next, we investigate a model with a monopoly medium; then we examine the effects of competition on informative reporting and factual content provision by analyzing a duopolistic model and comparing it with the monopoly model. 3. The Monopoly Medium We begin our analysis by studying the equilibrium under a monopoly medium. The medium’s objective is to maximize the profit. We further assume that the media have no incentive to misrepresent the message unless it is strictly profitable. The results show that as long as consumers value facts, the commercial incentives confound the ability of the medium to be fully informative. To show this, we first show that an equilibrium in which consumers are fully informed about the state can never exist. Definition 1: A fully informative equilibrium is a pure-strategy equilibrium such that if ] 1 , 0 [ , 2 1   t t with 2 1 t t  , and corresponding stances 1 s & 2 s with 2 1 s s  and   i i i t s t  |  , for 2 , 1  i . Lemma 1 A fully informative equilibrium does not exist unless 0  d . 70 Lemma 1 shows that the medium will not report the state fully informatively unless the consumers do not have divergent opinions about the state. The intuition behind this result is as follows. Because consumers value a report appeals to their own opinions (d >0), the medium has an incentive to fit the report to the consumers’ opinions and charge a higher price. If consumers believe the medium is fully informative, then it is always optimal for the medium to report the state with 2 1  s , regardless of what t is, in order to convince consumers that the state is 2 1 . Doing so not only increases consumers’ expectations about the number of facts but also best fits consumers’ opinions, which enables the medium to charge a higher price. Even though consumers desire to know the true state of the world, they anticipate the medium’s commercial incentives and therefore would not trust the medium to report fully informatively. From now on, we focus on the more interesting cases by assuming that 0  d . It is reasonable to wonder whether the non-existence of a fully-informative equilibrium is a direct implication of the assumption that consumers have no recourse if they catch a medium slanting their reports. But consumers, in our model are never misled. In fact, as long as d >0, consumers prefer some degree of slant over a fully accurate reports and would not take recourse. Although fully informative reporting equilibria are never possible, room still exists for consumers and the medium to construct a less-than-fully informative reporting equilibrium. We find that, more informative equilibria exist in which the space ] 1 , 0 [ is divided into several (smaller) intervals, and for different intervals the medium reports dissimilar media stances. We now consider the possibility of an equilibrium that is not fully informative. This can include the possibility that the medium’s reporting strategy is uninformative. Definition 2: A less-than-fully informative equilibrium in a monopoly is a Perfect Bayesian equilibrium (PBE) characterized by: 71  Reporting rules: There must be a media stance reporting profile vector with } , , , { ] 1 , 0 [ : 2 1 x s s s S   , where x is the number of intervals, for each medium, and a set of dividing points x i i a , , 0 ) (   with i i a a  1 , such that i s s  , for any ] , [ 1 i i a a t   .  Belief functions: These are consumers’ updated beliefs about the state of the world from the media stance, ) | ( i s t  .  Purchasing rules: Consumers will purchase reports from the media if the expected payoff is nonnegative. Hence the following purchasing rule applies:             otherwise , 0 0 , , if , 1 ) , , ( i i b i i b s p s n u E s p s n . (5)  Furthermore, (1) the reporting rules are optimal for the medium given the belief functions and purchasing rules, (2) the purchasing rules are optimal for consumers given the belief functions, and (3) the belief functions are derived from the reporting rules using Bayes’ rule whenever possible. The following proposition establishes the existence of a partially informative reporting equilibrium and fully characterizes it. We show that, as in CS, all reporting equilibria are interval equilibria in which the medium only reveals the state of the world to which the interval belongs. Proposition 1 A less-than-fully informative equilibrium is characterized by a set of dividing points with 1 0 1 1 0        x x a a a a  with 1  x , and a set of media stances x i i s , , 1 ) (   , where } , , 1 { ' , , ' x i i s s i i     such that: 1. x i i a , , 0 ) (   and x i i s , , 1 ) (   satisfies ) , , ( ) , , ( 1 1 1     i i i i i i a a s a a s   , for 1 , , 1   x i  where:                             2 1 1 2 2 1 2 2 2 1 1 1 if , ) ( if , ) 1 ( ) 1 ( 2 ) 1 ( 2 2 ) ( 1 ) , , ( i i i i i i i i i i i i i a z s d a z s d s a M s Ma M a a V a a s  (6); 72 2. ) , , ( max arg 1 i i s i a a s s    with ] , [ 1 i i a a s   for any ] , [ 1 i i a a t   ; 3. There is symmetry around the middle point: i x i a a   1 , i x i s s     1 1 for all x i , , 1   ; and 4. ) | ( i s t  is uniformly supported on ] , [ 1 i i a a  if ] , [ 1 i i i a a s   . Proposition 1 establishes necessary and sufficient conditions for the existence of a partition equilibrium in this setting. Although this equilibrium characterization closely resembles the one in the CS’s classic cheap-talk game, a significant difference exists. In our equilibrium, the choice of the media stance is NOT randomized within the interval. The reason for this distinction is due to the micro-foundation imbedded in our model. The media stance not only serves the function of affecting consumers’ expectations about the state but also directly affects their utility and corresponding WTP. Therefore, the medium is not indifferent to messages within an interval, as in CS. The optimal stance is unique within the interval and is affected by consumer preference parameters M and d. Figure 6 shows an example of the less-than-fully informative equilibrium with x intervals. For any possible t within a given interval, this stance may alter between intervals so that the media stances can signal to consumers about the interval of the state to which it belongs. Figure 6. Less-Than-Fully Informative Equilibrium with x Intervals 0 1 z 1-z 73 Next, we discuss two cases of Proposition 1. The first case is when there is only one interval (x = 1) so that the medium reports the same stance for any ] 1 , 0 [  t . As we can see, consumers cannot update their beliefs about the state of the world by observing the media stance. Therefore, this special case of a less-than-fully informative equilibrium is called the uninformative equilibrium, as shown in Fig. 7. Lemma 2 describes the medium’s profit and optimal choice of media stance when 1  x , and it also shows that when M is small enough we can expect the medium to report uninformatively. Figure 7. The Uninformative Equilibrium Lemma 2 There always exists an uninformative equilibrium, and the optimal stance for the monopoly is to report the state at 2 1  s , with the expected profit 2 2 1 2 ) ( z d V M      . Furthermore, there is a cutoff point 1 M such that when 1 0 M M   there only exists the uninformative equilibrium. Lemma 2 shows that in the uninformative equilibrium, the best choice of media stance is in the middle. That is because consumers cannot update the expected number of facts regardless of s, and the best the medium can do is to cater its stance as well as possible to consumers’ opinions by locating at the center of the ] 1 , [ z z  . It also shows that although an uninformative equilibrium always exists, when M is small enough, the monopoly reports are uninformative. Smaller intervals would indeed enable the medium to raise consumers’ expectations about the number of facts in the report. But if consumers do not value the facts ( 1 M M  ) then the medium 1 0 0.5 0.5 z 1-z 74 is unable to provide value by appealing to consumer opinion. Consumers are less inclined to interpret stances as meaningful for updating their expectations. The second case is when 2  x , which we refer to as the partially informative equilibrium. A specific example with 2  x is illustrated in Fig. 8. Under this example, the medium chooses a different media stance when the observed state falls into different intervals. More precisely, the medium will announce ] , 0 [ 1 a s  if ] , 0 [ a t  and ] 1 , [ 2 a s  if ] 1 , [a t  , where 2 1 s s  . Proposition 2 compares these two cases and shows when the medium can be rewarded for being more informative. Figure 8. A Partially Informative Equilibrium 0 1 z 1-z 75 Proposition 2 There exist two cutoff points, 2 M and 3 M ( 3 2 1 0 M M M    ), such that when 2 M M  there exists a partially informative equilibrium with 2  x as well as the uninformative equilibrium. When 3 M M  , the medium is better off in the partially informative equilibrium with 2  x . Proposition 2 shows that as consumers value facts more, it is possible for medium to be partially informative in equilibrium. It also says that the monopoly does not always benefit from producing partially informative reports even when it is possible. Only when M is large enough is it in the medium’s interest to increase communication efficiency and deliver a more informative report about the state to consumers. To illustrate the intuition, consider any interval ] , [ 1 i i a a  containing the state t and to left of 0.5. The stance that maximizes the number of facts is always left of the middle point of the interval 2 1 i i a a   . Recall that since 5 . 0  t , there are more facts with signal 0’s than with 1’s. So, while a stance of i a best appeals to consumer opinion, the medium can report more facts by shifting left toward the point that maximizes the number of facts. The optimal balance between these two effects is influenced by two parameters: M and d. When M increases, the optimal stance shifts left and closer to the position that maximizes the expected number of facts. This effect grows for t closer to 0. In fact, for the extreme case of the left most interval, when 0 1   i a , it is always profitable to reduce the chance i s t  since the medium might have nothing to report when 0  t . Hence the stance that maximizes the expected number of facts is actually a corner solution of 0 when ] , 0 [ 1 a t  . We can show when ) 1 ( 8 z d M   , the optimal stance for the medium in interval ] , 0 [ 1 a is 0. 76 We now define a measure of media informativeness as the extent to which the audience can infer the state of the world from seeing the stance. It also represents communication efficiency (Alonso et al. 2008, XS) between the media and consumers. Definition 3: Media informativeness is the residual variance of the state of the world:   2 ]) [ ( MI i t s t E t E    if the media report with i s when ] , [ 1 i i a a t   . This definition represents the residual uncertainty a consumer experiences after reading a report. We can see that as the medium reports become more informative (x = 1 vs. x = 2), the interval shrinks and MI increases. While there are multiple equilibrium when 2 M M  , Proposition 2 shows if 3 M M  , partially informative equilibria benefit both medium and consumers. Therefore from now on we focus on the Pareto efficient equilibrium as in CS, which is the most informative equilibrium. Following this mild refinement, consumers will have a better understanding about the state of the world and obtain more factual content when 3 M M  . 15 4. Competitive Media To understand the effect of media competition on media informativeness, we investigate a duopoly model and compare it with the previous monopoly case. One may first wonder whether competition forces media to be fully informative. 16 Proposition 3 tells us that the answer is no. 15 There are no explicit solutions for the partition of intervals for . Nevertheless, general results can be implicitly derived without any restrictions on x. An exception occurs in Section 5.3, where we must restrict attention to the cases of 2  x . 16 Our duopoly model is similar to a cheap-talk game with multiple senders. Battaglini (2002) showed that the fully revealing equilibrium is not stable when the information space is one-dimensional. Although others (Ambrus and Lu 2010, Lu 2011) have established the robustness of fully informative equilibria with multiple senders, our paper provides more insights on this important topic. Different from previous findings in standard cheap-talk game settings, we found first that a fully informative equilibrium can never exist in our framework. In what follows, we show that there is no equilibrium in which one or both media outlets are partially informative either. 2  x 77 Proposition 3 There does not exist a fully informative equilibrium with two competitive media. The intuition for this result is immediate. To see the intuition, suppose there is a fully informative equilibrium. Then, both media have identical stances located both at the state, with t s s B A   . In this case, media are undifferentiated substitutes and will engage into fierce Bertrand price competition and earn zero profit. A positive profit is possible by deviated to a different stance. It is useful to compare the intuition of this result to that of Lemma 1. In the monopoly case, the medium’s incentive to deviate from a fully informative stance arose purely from consumers’ opinions. With duopoly media taking fully informative stances, there are even stronger incentives to deviate due to competitive pressure. Despite the result that media are never fully informative in competition, the question remains as to whether there exists partially informative equilibriua. Before addressing this question we must define consumers belief-updating function after observing A s and B s , as well as what the out-of-equilibrium belief is with regard to the equilibrium. We first specify the equilibrium concept and the associated equilibrium belief. Because we have two media outlets, consumers’ purchasing rule can be affected by the media stance choices of the two media. We therefore need to provide a new definition of PBE under duopoly. With two media, A and B, a pure-strategy PBE is characterized by: 78  Reporting rules: A media stance profile vector for each medium } , { B A l  with } , , , { ] 1 , 0 [ : 2 1  l l l s s S  , and a set of dividing points x i l i a , , 0 ) (   with l i l i a a 1   , such that l i s t s  ) ( for any ] , [ 1 l i l i a a t   .  Belief functions: Consumers’ updating of beliefs about the state of the world from the media stance ) , | ( B i A i s s t  .  Purchasing rules:                       otherwise , 0 , , , , and , 0 , , if , 1 ) ( B i B B i B b A i A A i A b A i A A i A b A b s p s n u E s p s n u E s p s n u E . (7) It requires that (1) reporting rules must be optimal for the media given the belief functions and purchasing rules, (2) purchasing rules must be optimal for consumers given the belief functions, and (3) the belief functions must be derived from the reporting rules using Bayes’ rule whenever possible. Definition 4: A partially informative equilibrium with two competitive media is a pure- strategy equilibrium if there exists a media stance profile vector for each medium with } , , , { ] 1 , 0 [ : 2 1  l l l s s S  , } , { B A l  for each medium and a set of dividing points x i i a , , 0 ) (   with 2  x , so that l i l s t s  ) ( for any ] , [ 1 i i a a t   , that the media choice is optimal for both media and that ) , | ( B A s s t  is uniformly supported on ] , [ 1 i i a a  if ] , [ , 1 i i B A a a s s   . If a partially informative equilibrium with two media exists, we can conclude that it is possible for consumers to partially infer the state of the world from the media reporting. However, our next proposition shows a different result. 79 Proposition 4 There does not exist any partially informative equilibrium with two competitive media. Neither medium has an incentive to stay with another medium in the same interval. When one medium is partially informative, the other medium has an incentive to “jam” the stance of its rival by choosing a media stance from another interval. Consumers see stances from different intervals and are therefore unable to update their beliefs. Jamming implies that consumers consider both media uninformative. Because jamming is a crucial and effective strategy in the duopoly case, we provide an elaboration of the jamming strategy. Assume consumers believe that both media report informatively. Based on consumers’ beliefs, whenever medium A chooses A s from ] , [ 1 i i a a  and medium B chooses B s from ] , [ ' 1 ' i i a a  , so that there is no overlapping between the intervals ] , [ 1 i i a a  and ] , [ ' 1 ' i i a a  , these two media stances are conflicting since it is impossible to have a state of the world from both ] , [ 1 i i a a  and ] , [ ' 1 ' i i a a  . Therefore, consumers cannot infer which medium is actually informative about the state of the world under conflicting media reporting. As a result, consumers have no means to update their beliefs about the state. Given Proposition 4, we know it is impossible to find an equilibrium in which both media are informative. Thus, the only possible cases are when one media is partially informative and the other is uninformative or when both media are uninformative. In order to explore the optimal choice of media stance in both cases, we need to filter implausible equilibria in our PBE. The reason is that the definition of PBE puts very little constraint on consumers’ beliefs as long as they support the equilibrium. While we can use the Bayes’ rule to characterize consumer equilibrium beliefs with one medium, theoretically there are an infinite number of stance 80 combinations with multiple senders, which offers no clear prediction about the likely outcome. For example, consumers can believe that any random stance 1 s between ) , 0 [ 2 1 indicates that ] , 0 [ 2 1  t , while 1 2 1 s s   indicates that ] 1 , [ 2 1  t , and they can believe that any other choices of media stance are uninformative. Hence, we refine our selection of equilibria to find the most stable one. 17 The refinement we introduce, the “favorable criterion,” provides a means to select the most intuitive equilibrium. Like refinements in other signaling games, the favorable criterion filters out equilibria supported by implausible out-of-equilibrium beliefs. The favorable criterion relies on the following characterization of beliefs. Definition 5: A consumer’s out-of-equilibrium belief is a favorable belief if, for any equilibrium deviation by a medium, consumers acting under this belief (weakly) increase their expectation of the number of facts that will be reported by that medium. For example, if in equilibrium the optimal choice of media stance is A s , then given the equilibrium belief, consumers expect that medium A has A n facts. However, if medium A chooses a media stance A s ~ different from A s , then a favorable belief is any belief such that the medium’s expected number of facts under the belief is A A n n  ~ . Definition 6: An equilibrium satisfies the favorable criterion if for any deviations from the equilibrium path the media’s payoff is strictly decreasing under some favorable out- of-equilibrium belief, all else being equal. 17 In the game-theory literature, this is typically achieved by implementing an established equilibrium-refinement criterion. For example, the intuitive criterion has been shown to be an effective refinement in signaling games with two types. In the cheap-talk literature with multiple senders there is unfortunately no commonly accepted criterion on equilibrium refinement (Battaglini 2002). In addition, given that our setting is actually a combination of cheap- talk and location model, it is impossible to find existing criteria that can be effectively implemented into our new setting. 81 From this definition, we can see that if an equilibrium fails the favorable criterion it means that any favorable out-of-equilibrium belief rewards the deviation. Then the medium can make a statement like the following to consumers: “If I choose a media stance A s ~ , you should believe I generate at least as many facts as A s because as long as you believe the number of facts of the new report is (weakly) higher, my payoff is no less than what I obtained before. In this way, we will deviate from the equilibrium to provide a report with (weakly) more facts, and thus you should believe me.” As we can see, this criterion is essentially asking consumers to use forward induction (Cho and Kreps 1987, Gibbons 1992) when interpreting a stance choice. When consumers form the updated belief, they ask whether the medium’s choice is rational, which means a deviation from the equilibrium path should at least not decrease the medium’s payoff if consumers believe that this deviation brings more facts. Therefore, the statement of deviation is credible. If the equilibrium satisfies this criterion, then there exists at least one favorable out-of- equilibrium belief that could reduce the medium’s payoff if the medium deviates from the equilibrium. Hence, this above statement is not “credible” any more since not all favorable out- of-equilibrium beliefs can benefit from the deviation. As we can see, this equilibrium refinement can help us to find the most stable and credible equilibrium. To see how this criterion works, we examine an example. Suppose an equilibrium belief indicates that consumers always believe that media stance 3 1  s represents ] , 0 [ 2 1  t and that 3 2  s represents ] 1 , [ 2 1  t —in other words, consumers believe that any other choices of media stances are not informative. We can see that there exist at least two types pure-strategy PBEs under this set of equilibrium beliefs. Let’s further assume that B A s s  . The first one is 3 1  A s and 3 2  B s . Under this case, consumers do not know which medium is actually partially 82 informative because stances are exactly mirror opposites from different intervals. Hence, 0 ) (     B A n n . Now, if medium A deviates from the equilibrium by choosing ) , , ( max arg ~   B A A s A s s s A  , then consumers’ favorable out-of-equilibrium belief is to believe that medium A is either still uninformative or partially informative. If the belief is the former, then we know that ) , , ( ) , , ~ (    B A A B A A s s s s   . Otherwise, if consumers believe medium A is partially informative,    ~ . Therefore, ) , , ( ) , , ~ ( ) ~ , , ~ (      B A A B A A B A A s s s s s s    , and hence this equilibrium does not pass the favorable criterion unless 3 1 ~   A A s s . Another possible equilibrium is one in which a medium reports based on the equilibrium belief and another medium reports uninformatively. Let us assume that A is informative and chooses 3 1  A s when ] , 0 [ 2 1  t . Since media B is uninformative, we know that 0   . Medium B will choose ) , , ( max arg   B A B s B s s s B  . Now, if medium A deviates from A s , then it can be profitable by choosing ) , , ( max arg ~   B A A s A s s s A  . A favorable out-of-equilibrium belief is that A reports at least the same number of facts as before, so that    ~ . Then, ) , , ( ) , , ~ ( ) ~ , , ~ (      B A A B A A B A A s s s s s s    . Hence, we can always find a deviation that could benefit medium A given the favorable out-of-equilibrium belief unless 3 1 ~   A A s s . Similarly, we can show that there exists a deviation for medium B given the favorable out-of-equilibrium belief unless 3 2 ~   B B s s .Therefore, we can see that the favorable criterion can effectively filter out any equilibrium in which one medium’s choice of stance is not an optimal response to the other given the equilibrium belief. Otherwise, a medium can always benefit from deviation. Therefore, we can narrow down the choice of media stance into two possible sets of equilibria in which both media’s stances are optimal given the other medium’s stance and 83 consumer beliefs: (1) an asymmetric equilibrium in which one medium is partially informative and the other is uninformative, and (2) one in which both media are uninformative. We first show that case (1) is impossible due to the threat of jamming. Then we characterize the optimal media stances under the second case. Proposition 5 There does not exist any asymmetric equilibrium in which one medium is uninformative and the other medium is partially informative under the favorable criterion. The intuition for this proposition is the following: if there existed an equilibrium in which only one medium reports partially informatively, then consumers would believe the uninformative medium provides fewer facts than the other medium. The uninformative medium suffers a profit loss from the lower expectation of the number of facts that will be in its report. Therefore, it has an incentive to jam the other medium by taking the “mirror” stance, so that consumers do not know which medium is actually partially informative. Our result shows that the uninformative medium always benefits from jamming, and that this incentive for deviation becomes stronger as M enlarges. Therefore, consumers should not believe any medium is partially informative in equilibrium implying that an asymmetric equilibrium is impossible. 18 Proposition 6 There exists a unique uninformative equilibrium that satisfies the favorable criterion. The optimal choice of media stance (assuming B A s s  ) is given by } 0 ), 2 1 ( max{ 4 3 2 1 z s A    and } 1 ), 2 1 ( min{ 4 3 2 1 z s B    . 18 Although our model is a one shot game, we can consider a dynamic model with reputation for a certain position, perhaps influenced by its previous choices of slant. Incorporating such dynamics reinforces the results from this static model. 84 This proposition establishes the existence and uniqueness of an equilibrium with two competitive media. Furthermore, it characterizes the stances in an uninformative equilibrium for both media. Interestingly, since both media are uninformative and have an equal expected number of facts, the equilibrium stance in this case is independent of consumers’ valuation of facts (M) and instead is only decided by the heterogeneity of consumer opinions (z). A graphical example is shown in Fig 9. Figure 9. Uninformative Equilibrium with Two Media 0 1 0.5 z 1-z 85 5. Competition vs. Monopoly In this section, we compare the equilibrium results of the monopoly and duopoly cases by first examining whether competition improves media informativeness and factual content provision. Next, we examine whether competition causes media reporting to be more polarized. Finally, we extend the scope of the analysis to incorporate the concept of media bias into our model and examine how competition affects it. 5.1 Media Informativeness and Factual Content Provision In this section, we focus on the comparison of media informativeness and content provision under the monopolistic and duopolistic cases. Propositions 2 & 4-6 indicate that competition deteriorates media informativeness, especially when consumers value facts more. Proposition 7 Competition does not increase the informativeness of media reporting when 1 M M  , but it decreases the informativeness when 3 M M  . Proposition 7 says that competitive commercial media leave consumers less informed. Since duopolistic media are always uninformative, the informativeness is (weakly) lower under competition. The competitive environment prevents each medium from being even partially informative. Even if one medium tries to report informatively, competition encourages the other medium to “jam” its stance by taking an equal but opposing stance in order to neutralize the rival’s advantages of being believed to have more facts. This is a counter example to Shaked and Sutton (1982, 1983)’s vertical differentiation case, in which they showed that media can have an incentive to differentiate themselves by quality. In our framework, even though we allow that the product quality (the number of facts) to be endogenously chosen, any efforts to build up the (vertical) advantage in content reporting through staying partially informative will be offset by 86 the rival’s jamming behavior. While the single medium benefits from reporting informatively when consumers value the facts, this incentive disappears with competition. Hence, competition reduces the communication efficiency—the additional voice actually confuses consumers. Next, we study the impact of competition on the factual content provision. The following proposition indicates that competition decreases the average provision per medium. Proposition 8 Relative to a monopoly medium, a competitive medium reports strictly fewer facts when 3 M M  . Our results indicate that a medium becomes less informative and reports fewer facts under competition. This last finding may provide an alternative explanation of why micro- blogging platforms such as Facebook, Twitter, and Tumbler have become so popular. A competitive environment drives the media to reduce product quality in the form of the factual content provision. The reduction of factual content leads to an increased need for micro-blogging platforms, which restrict the amount of factual information that each medium can provide, in order to conceal the reduction information provided. This competitive reason for the booming of the micro-blogging industry has never been examined in the previous literature. 5.2. Media Polarization We call a media stance more polarized if the stance significantly diverges from the middle point of the state. Specifically, for any equilibrium stance in monopoly, s define the polarization measure | | 2 1   s MP Mon . And for any pair of equilibrium stances in duopoly, B A s s , which are symmetric around the middle point by Proposition 6, the corresponding measure is   | | | | 2 1 2 1 2 1     B A Duo s s MP , which is the average distance of media stances from ½. Both MS and XS find that competition pushes media stances toward more extreme positions. Our result is 87 consistent with their finding, but only under certain conditions. If those conditions do not hold, competition does not necessarily drive the media to be more polarized. Proposition 9 Competition does not necessarily imply that media stances are more polarized. i) When z and M are large enough, monopoly is more polarized than duopoly Duo Mon MP MP  . ii) When z and M are small enough, duopoly is more polarized than monopoly Duo Mon MP MP  . The intuition of the proposition is based on the different driving forces for the choice of stance under different competitive environments. Under monopoly, the medium’s reporting depends on consumers’ preference for facts (M). When M is large enough, the monopoly provides partially informative reports, and therefore the stance is within the intervals. A higher M drives the stance further away from the middle point. However, the duopolistic media are always uninformative. The stances are only decided by the degree of consumer heterogeneity (z). When z is large, the stance by each medium is closer to the middle point. Therefore, when z and M are large enough, monopoly is more polarized than duopoly. But if z and M are small enough, the media stance of monopolistic media is positioned at the middle point. At the same time, duopolistic media position themselves toward the endpoints to accommodate diverse consumer opinions. Therefore, monopoly is less polarized than duopoly in this case. One thing we want to emphasis here is that this result is not simply a maximum differentiation result (MS, XS). Although the competitive equilibrium outcome is quite similar, the underlying reason is very different. The rival takes a mirror stance to eradicate the 88 informative medium’s competitive advantage and to focus readers’ choices solely on opinions. Even though competitive media may take opposite positions, they do so only to the extent of heterogeneity in consumer opinion. Also, our result, which is different from previous findings, indicates that a monopoly medium’s stance is more polarized than a duopolist’s under certain conditions. 5.3 Media Bias and Media Competition Relative to previous research, the results of our analysis provide new insights regarding the relationship between media bias and the degree of competition. Earlier work, notably MS and XS, define media bias as a relative measure of the distance between the state and the media stance (e.g. MS, XS), which captures the distortion of a media position. Because those works do not permit consumers to update beliefs about the state based on media strategies, they are unable to tell whether consumers obtain better understanding from reading a media report, nor how consumers make inferences about the state from the distorted information. To understand how these distinctions matter, we must redefine media bias to account for consumers’ inference. Media bias in our model is measured by the weighted distance between the media stance and the state of the world. Definition 7: Media bias is the expectation of weighted distance by which the media stance deviates from the state of the world:     1 2     i i i a a t s t E MB , if the media reports with i s when ] , [ 1 i i a a t   . An important aspect about this definition of media bias is the denominator of ) ( 1   i i a a . This enables us to compare media bias under different informative levels. The measure of media bias used by MS or XS is not suitable in our setting because it does not adjust for consumers’ 89 ability to identify the interval from which the state lies. Therefore, we normalize the expected difference by the size of the updated interval. Also, in order to compare the media bias in different informative levels, a full characterization of the interval structure is necessary. However, it is impossible to obtain tractable solutions for the intervals when 2  x . Hence we restrict our attention in the following examples to 2  x in this section. Using this measure of media bias, we find two results: (i) a higher informative reporting does not necessary lead to lower media bias, and (ii) competition can actually reduce it. Proposition 10 When ) 1 ( 8 z d M   , the partially informative reporting with x=2 in monopoly has higher media bias than uninformative reporting. (a) Uninformative (b) Partially informative with two intervals Figure 10. Media Bias in Monopoly under Different Informative Level Normally we would think a more informative report should be less biased. Proposition 10 shows this is not always the case. The fundamental conflict in consumers’ preferences drives this result: consumers want to read more facts, but at the same time like to read a report appealing to their opinions. A more informative reporting strategy certainly raises consumer expectation about the facts, but at the same time, the medium still has an incentive to appeal to consumer 0 1 0.5 z 1-z 0 1 0.5 0.75 0.25 z 1-z 90 opinion, which forces it to report the state of the world towards the expectation of consumer opinions. The dispersion between the updated expectation of the state of the world and the expectation of consumer’s opinion will be higher as consumers’ preference for facts increases. As a result, the polarization becomes stronger when M is large enough, which increases the media bias. Figure 10 shows the disparity of media informativeness and media bias under different reporting equilibria. The first picture is when the reporting is uninformative. From Lemma 2 we know the optimal media stance is 0.5, which minimizes the media bias of the uninformative equilibrium. On the other hand, following the discussion about the choice of the media stance in section 3, in a partially informative reporting equilibrium with two intervals, when ) 1 ( 8 z d M   , the medium chooses a media stance 0 1  s when t belongs to ] 5 . 0 , 0 [ .We can clearly see that 1 s is very polarized relative to either the old expectation of the state (0.5) or the new expectation (0.25), which demonstrates the increase of media bias with more informative reporting. Proposition 10 illustrates the fundamental difference between the media informativeness and media bias, and shows how a report with higher media bias can still be more informative. Proposition 10 also shows that the media bias concept is not an ideal measure of the quality of communication between media and consumers. The medium can be “biased but informative” at the same time, which challenges the use of media bias as a measure of consumers’ ability to be informed. The last proposition summarizes the findings regarding media bias and competition. 91 Proposition 11 Competition does not necessary increase media bias. i) When z and M are large enough, the partially informative equilibrium with 2  x under monopoly has higher media bias than duopoly: Duo Mon MB MB  . ii) When z and M is small enough, monopoly has lower media bias than duopoly Duo Mon MB MB  . Starting from MS, a common result in the literature is that competition increases the media bias by the principle of maximum horizontal differentiation. Our framework echoes the previous finding, but only under certain boundary conditions. The fundamental reason for this result is again because a medium can be biased but informative. Proposition 10 establishes the uninformative equilibrium in monopoly might have lower media bias than the more informative equilibrium. Therefore, if z is high enough, the media bias of a duopoly is closer to the media bias of the uninformative equilibrium in monopoly. However, if M is large, the monopoly medium reports partially informatively and can have higher media bias than in the uninformative equilibrium. That explains why the media bias of monopoly is higher than the duopoly when z and M are large enough. The intuition of the second result is similar but opposite. 92 (a) Monopoly (x=2) (b) Duopoly Figure 11. Media Bias Comparison under Competition (z and M are large) 6. Implications and Discussions Our results suggest that encouraging competition in the commercial media market does not necessarily make consumers better informed. This result is consistent with recent survey evidence about how informed consumers are depending on their news source. For example, one study found that Fox News and MSNBC viewers are the least informed about current events compared with those who use other news sources. 19 The result from Section 5.1—that competitive forces encourage media to take stances that compromise their ability to produce factual content—may have an interesting connection to the growth of micro-blogging sites such as Facebook, Twitter and Tumblr, which limit the amount of content users can provide. These forms of media may have gained popularity because of heavy competition for consumer attention, which are arguably due to the internet lowering the barriers to content provision. While publishers on those platforms do not typically collect 19 http://www.forbes.com/sites/kenrapoza/2011/11/21/fox-news-viewers-uninformed-npr-listeners-not-poll-suggests/. http://www.huffingtonpost.com/2012/05/23/fox-news-less-informed-new-study_n_1538914.html. Accessed May 2012. 0 1 93 monetary transfer from consumers, they do benefit from additional consumer attention, which is obviously a scarce resource (e.g. a twitter is better off with more followers). In light of our results, heavier competition encourages media to switch to microblogging platforms since they can deliberately obscure the reduction of content provision. Another interesting finding in this paper is that a balanced report (for example: a media article claims global warming is inconclusive and put equal amount of facts from both sides) does not necessarily facilitate viewers’ understanding about the state of the world. Some research attributes balanced reporting as implied by journalistic norms and values (Boykoff & Boykoff 2004), but our paper points to a different explanation. When readers value balanced reports more highly than unbalanced reports (as is the case in our model when 0  M , the media have an incentive to align their content to consumer opinions). In this way, a medium’s incentive to appeal to balanced reporting causes a divergence between the general scientific discourse and viewer attitudes toward it. That is, the media could simultaneously be balanced, yet uninformative. In the case of global warming, for example, if scientists generally accept that global warming is occurring (t~1) but consumers prefer balanced reporting over factual content, then a medium has a tendency to slant content toward a balanced angle indicating that global warming’s occurrence is inconclusive. On the other hand, as this paper shows, an unbalanced report under monopoly can be more informative than a balanced report, which implies that biased reporting does not leave viewers with less knowledge. The important thing to keep in mind is that a media stance that is polarized is not always meaningless, as long as there are no jamming voices opposing it. A provocative report, even though it is biased, could tell consumers more about current events than a plain and “politically neutral” one, when competition among commercial media is not high. 94 Finally, our model can be used to understand the implication of “cross-checking” – the notion that consumers read multiple media to obtain different perspectives. MS (2005) suggests that, by reading both media, “a conscientious reader gets all the facts, as if she were able to read an unslanted newspaper.” Our paper indicates that conscientious readers do not necessarily learn all the facts by cross checking different media. The reason is that when the state lies on one side of both media stances, the media will use either all the facts with signal “1”s or “0”s, but not both. Hence reading both media does NOT guarantee that readers read all the facts. It is only when the state is located between both media stances 20 that conscientious readers obtain all the facts. Since when media stances are more polarized as z decreases, consumers’ heterogeneous opinions help conscientious readers to be more informed. Also, the average media bias increases as media stances are more polarized, which means that conscientious readers are more informed when the media are more biased (this intuition is very similar to XS). This finding again echoes the counterintuitive relationship between media informativeness and media bias. 7. Conclusions & Limitations This paper has presented the first analysis of selective factual content provision by commercial media. Our model differs from previous research by incorporating the following elements (1) Factual content provision is bounded by the choice of media stance. (2) Consumers appreciate more facts. (3) Consumers can (partially) infer the state from the media stance. We find that while the commercial incentives of media prevent the monopoly from being fully informative, it can help consumers to understand the state of the world better by providing informative reporting. In contrast, readers facing competitive media end up learning little or nothing and read fewer facts. We also find several other counterintuitive results: competition does not cause the media 20 Mathematically: B A s t s   . 95 stance to be more extreme when consumers value facts and are less diverse, a more-informative report does not necessarily lead to a lower media bias, and competition can reduce media bias. We related our results to anecdotal evidence and shed light on media regulation, the booming of micro-blogging, and other important subjects related to selective factual content provision by commercial media. One important assumption we made is that the state of the world is unidimensional. However, it is natural to consider a multidimensional state space. For example, the controversial issue of global warming involves issues related not only to climate change but also to the development of alternative energy sources. Battaglini’s (2002) analysis of standard “cheap-talk” in a multidimensional state space may provide some guidance. He shows, in fact, that multidimensionality can improve communication efficiency with multiple senders. Intuitively, multidimensionality can soften the conflicts among information senders and, therefore, leave room for senders to coordinate. Future work can extend our framework by considering the case in which the state is conceived as having more than one dimension. In this paper, we considered a setting in which the media do not have any preference about the stance. This allows us to isolate the impact of competition on factual content from other factors. However, it is not hard to imagine that the media itself is not perfectly neutral about the stance. Several studies (Balan et al. 2004, Baron 2004, Anderson & Mclaren 2009) provide insight on the supply side analyses of media reporting with media owners having preferences about what consumers should read. We do not anticipate that the introduction of media preference will alter the main driving force of the main result: media optimally balance consumers’ desire for facts and their taste for slant. It would still be interesting to investigate, 96 however, whether the media would be less or more informative when the goal of reporting is considered to be not exclusively profits. 97 REFERENCES Agarwal, N., S. Athey, D. Yang. 2009. Skewed Bidding in Pay Per Action Auctions for Online Advertising. American Economic Review Papers & Proceedings, 99(2) 441-447. Aggarwal, G., A. Ashish, R. Motvani. 2006. Truthful Auctions for Pricing Search keywords. Proceedings of the 7th ACM Conference on Electronic Commerce. Alonso, Ricardo, Wouter Dessein and Niko Matouschek. 2008. When Does Coordination Require Centralization? American Economics Review, 98(1): 145-179. Ambrus, Attila and Shih En Lu. 2010. Robust Almost Fully Revealing Equilibria in Multi- Sender Cheap Talk. Working Paper, Harvard University. Anand, Bharat, Rafael D. Tella and Alexander Galetovic. 2007. Information or Opinion? Media Bias as Product Differentiation. Journal of Economics and Management Strategy, 16(3): 635-682. Anderson, E. T., D. I. Simester. 1998. The Role of Sale Signs. Marketing Science, 17 (2), 139- 155. Anderson, Simon and Stephen Coate. 2005. Market Provision of Broadcasting: A Welfare Analysis. Review of Economics Studies, 72(4): 947-972 Anderson, Simon and John Mclaren. 2009. Media Mergers and Media Bias with Rational Consumers. Working Paper, University of Virginia. Athey, S., G. Ellison. 2008. Position Auctions with Consumer Search. Unpublished manuscript, MIT. http://econ-www.mit.edu/files/2879 Balan, David J., Patrick DeGraba and Abraham L. Wickelgren. 2004. Ideological Persuasion in the Media. Working Paper, University of Texas at Austin. 98 Baltas, G. 2003. Determinants of Internet Advertising Effectiveness: an Empirical Study. International Journal of Market Research. 45(4) 505-513. Baron, David P. 2004. Persistent Media Bias. Journal of Public Economics, 90(1): 1–36. Battaglini, Marco. 2002. Multiple Referrals and Multidimensional Cheap Talk. Econometrica, 70(4): 1379-1041. Battelle, J. 2005. The Search: How Google and its Rivals Rewrote the Rules of Business and Transformed our Culture. Penguin Books, London, England. Bhardwaj, Pradeep, Yuxin Chen and David Godes. 2008. Buyer-Initiated vs. Seller-Initiated Information Revelation. Management Science, 54 (6) 1104-1114. Blackwell, D. (1965). Discounted Dynamic Programming. Annals of Mathematical Statistics 36(1) 226-235. Borgers, T., I. Cox, M. Pesendorfer, V. Petricek. 2007. Equilibrium Bids in Sponsored Search Auctions: Theory and Evidence. Unpublished manuscript, University of Michigan. http://www.adastral.ucl.ac.uk/~icox/papers/2007/Auction.pdf. Boykoff, Maxwell and Boykoff. Jules. 2004. Balance as Bias: Global Warming and the US Prestige Press. Global Environmental Change. 14(2): 125-36. Chandon, J. L., M. S. Choutou, D. R. Fortin. 2003. Effects of Configuration and Exposure levels on Responses to Web Advertisements. Journal of Advertising Research. 43(2) 217-229. Chen, J., D. Liu, A. B. Whinston. 2009. Auctioning Keywords in Online Search. Journal of Marketing, 73 (July), 125-141. Chen, Y., C. He. 2006. Paid Placement: Advertising and Search on the Internet. Unpublished manuscript, NET Institute. 99 Chen,Y., N. Kartik and J. Sobel. 2008. Selecting Cheap-Talk Equilibria. Econometrica, 76(1): 117-136. Cho, I. and D. M. Kreps. 1987. Signaling Games and Stable Equilibria. Quarterly Journal of Economics, 102(2): 179-222. Chu, W. 1992. Demand Signalling and Screening in Channels of Distribution. Marketing Science, 11 (4), 327-347. Clarke, E. 1973. Multipart pricing of public goods. Public Choice, 11, 17-33. Danaher, P. J., G. W. Mullarkey. 2003. Factors Affecting Online Advertising Recall: a Study of Students. Journal of Advertising Research 43(3) 252-267. Desai, P. S. 2000. Multiple Messages to Retain Retailers: Signaling New Product Demand. Marketing Science, 19 (4), 381-389. Dré ze, X., F. Husherr. 2003. Internet Advertising: Is Anybody Watching? Journal of Interactive Marketing 17(4) 8-23. Edelman, B., H. S. Lee. 2008. CPC/CPA Hybrid Bidding in a Second Price Auction. HBS Working Paper 09-074. Edelman, B., M. Ostrovsky, M. Schwarz. 2007. Internet Advertising and the Generalized Second-Price Auction: Selling Billions of Dollars Worth of Keywords. American Economic Review 97(1) 242-259. Eldon, E. 2010. Facebook Revenues Up to $700 Million in 2009, On Track Towards $1.1 Billion in 2010. http://www.insidefacebook.com/2010/03/02/facebook-made-up-to-700-million- in-2009-on-track-towards-1-1-billion-in-2010/ Ellman, M. and F. Germano. (2009).What Do the Papers Sell? A Model of Advertising and Media Bias. Economic Journal, 119: 680-704. 100 Evans, D. 2008. The Economics of the Online Advertising Industry. Review of Network Economics, 7 (3), 359-391 Even-Dal, E., M. Kearns, J. Wortman. 2007. Sponsored Search with Contexts. Proc. of the 3rd International Workshop on Internet and Network Economics (WINE 2007). Facebook.com. 2010. Press room. http://www.facebook.com/press/info.php?statistics. Accessed August 2010. Feng, J., J. Xie. 2007. Performance-Based Advertising: Price and Advertising as Signals of Product Quality. Unpublished manuscript, University of Florida. http://papers.ssrn.com/sol3/papers.cfm? abstract_id=1027296 Fudenberg, D. and J. Tirole. 1986. A “Signal-Jamming” Theory of Predation. Rand Journal of Economics, 17(3): 366-376. Fudenberg, D., J. Tirole. 1991. Game Theory. The MIT Press. Cambridge. USA. Gal-Or, E. and A. Dukes. 2003. Minimum Differentiation in Commercial Media Markets. Journal of Economics and Management Strategy, 12(3): 291-325. Gal-Or, E., T. Geylani and T. P. Yildirim. 2012. The Impact of Advertising On Media Bias. Journal of Marketing Research, 49(1):92-99. Gardete, P. M. 2012. Cheap-Talk Advertising and Misrepresentation in Vertically Differentiated Markets. Marketing Science, forthcoming. Gentzkow, M. and J. M. Shapiro. 2006. Media Bias and Reputation. Journal of Political Economy, 114(2): 280-316. Gentzkow, M. and J. M. Shapiro. 2010. What Drives Media Slant? Evidence from U.S. Daily Newspapers. Econometrica, 78(1): 35-71. 101 Ghose, A., S. Yang. 2009. An Empirical Analysis of Sponsored Search Advertising: Sponsored Search in Electronic Markets. Management Science, 55 (10), 1605-1622. Gilligan, T. W. and K. Krehbiel. 1989. Asymmetric Information and Legislative Rules with a Heterogeneous Committee. American Journal of Political Science, 33(2): 459-490. Gibbons, R. 1992. Game Theory for Applied Economists. Princeton University Press. Goel, A., K. Munagala. 2009. Hybrid Keyword Search Auctions. Proc. 18 th World Wide Web Conf. (WWW). http://arxiv.org/abs/0807.2496. Godes, D., E. Ofek and M. Sarvary, “Content vs. Advertising: The Impact of Competition on Media Firm Strategy,” Marketing Science, 28(1): 20-35 Goldfarb, A., C. Tucker. 2007. Search Engine Advertising: Pricing Ads to Context. Unpublished manuscript. http://papers.ssrn.com/sol3/papers.cfm? abstract_id=1021451 Goldfarb, A., C. Tucker. 2009. Online Display Advertising: Targeting and Intrusiveness. Marketing Science, forthcoming. Google Inc. 2010. 2009 Annual Report. http://investor.google.com/pdf/ 2009_google_annual_report.pdf. Accessed August 2010. Groseclose, T. and J. Milyo. 2005. A Measure of Media Bias. Quarterly Journal of Economics, 120(4): 1191-1237. Groves, T. 1973. Incentives in teams. Econometrica, 41 (4), 617-631. Hayakawa, S. I.. 1990. Language in Thought and Action. 5th ed. Harcourt Brace Company, New York. He, C., Y. Chen. 2006. Managing e-Marketplace: a Strategic Analysis of Non-price Advertising. Marketing Science 25(2) 175-187. 102 Henry, E. 2009. Strategic Disclosure of Research Results: the Cost of Proving Your Honesty. Working Paper, London Business School. Intergovernmental Panel on Climate Change. 1990. First Assessment Report. Accessed at <http://www.ipcc.ch/ipccreports/far/wg_I/ipcc_far_wg_I_full_report.pdf> on May 2012. Hu, Y. 2004. Performance-based Pricing Models in Online Advertising. Unpublished manuscript, Purdue University. http://papers.ssrn.com/sol3/papers.cfm?abstract_id=501082 Hu, Y., J. Shin, Z. Tang. 2010. In Search of the Holy Grail of Online Advertising: Cost per Click versus Cost per Action. Unpublished manuscript, Purdue University. Jerath, K., L. Ma, Y. Park, K. Srinivasan. 2010. A “Position Paradox” in Sponsored Search Auctions. Unpublished Manuscript, CMU. http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1464545 Katona, Z., M. Sarvary. 2008. The Race for Sponsored Links: A Model of Competition for Search Advertising. Marketing Science, forthcoming. Keane, M. 2010. Facebook’s ad changes could cost CPM advertisers. http://econsultancy.com/blog/5849-facebook-s-ad-changes-could-cost-cpm-advertisers. Accessed August 2010. Kempe, D., M. Mahdian. 2007. A Cascade Model for Externalities in Sponsored Search. Proceedings of WINE 2008. http://www-rcf.usc.edu/~dkempe/publications/cascade.pdf Krishana, V. and J. Morgan. 2001. A Model of Expertise. Quarterly Journal of Economics, 116(2): 747-775. Krishnamurthy, S. 2000. Deciphering the Internet Advertising Puzzle. Marketing Management. 9(3) 35-39. 103 Libai, B., E. Biyalogorsky, E. Gerstner. 2003. Setting Referral Fees in Affiliate Marketing. Journal of Service Research, 5(4) 303-315. Lohtia, R., N. Donthu, E. K. Hershberger. 2003. The Impact of Content and Design Elements on Banner Advertising Click-Through Rates. Journal of Advertising Research 43(4) 410-418. Lu, S. E. 2011. Coordination-Free Equilibria in Cheap Talk Games. Working Paper, Harvard University. Mayzlin, D. and J. Shin. 2011. Uninformative Advertising as an Invitation to Search. Marketing Science, 30(4) 666-685. Milgrom, P. 2003. Putting Auction Theory to Work: the Simultaneous Ascending Auction. Journal of Political Economy 108(2) 245-272. Moorthy, S., K. Srinivasan. 1995. Signaling Quality with a Money-Back Guarantee: the Role of Transaction Costs. Marketing Science, 14 (4), 442-466. Munarriz, R. A. 2010. Bing and Google Gang up on Yahoo! http://www.fool.com/investing/high-growth/2010/03/10/bing-and-google-gang-up-on- yahoo.aspx Mullainathan, S. and A. Shleifer. 2005. The Market for News. American Economic Review, 95(4): 1031-1053. Nazerzadeh, H., A. Saberi, R. Vohra. 2008. Dynamic Cost-per-Action Mechanisms and Applications to Online Marketing, Proceedings of the WWW 2008 Conference. http://www.stanford.edu/~saberi/cpa.pdf. Newcomb, K. 2005. Google’s CPM Ads Meet Lukewarm Reception. ClickZ, April 27. http://www.clickz.com/3500856, accessed July 2009. 104 Nielsen. 2009. Global Faces and Networked Places. http://blog.nielsen.com/nielsenwire/ wp- content/uploads/2009/03/nielsen_globalfaces_mar09.pdf. Accessed March 2009. Oreskes, N. 2004. The Scientific Consensus on Climate Change. Science, 306(5702):1686. Osborne, M. J. 2004. An Introduction to Game Theory. Oxford University Press: New York. Robinson, H., A. Wysocka, C. Hand. 2007. Internet Advertising Effectiveness. International Journal of Advertising 26(4) 527-541. Robinson, M. J. 2007. Two Decades of American News Preference. Pew Research Center on the People and the Press. Accessed at <http://pewresearch.org/pubs/566/> May 2012. Rutz, O., R. Bucklin. 2007a. A Model of Individual Keyword Performance in Paid Search Advertising. Unpublished manuscript, Yale University. Rutz, O., R. Bucklin. 2007b. From Generic to Branded: a Model of Spillover Dynamics in Paid Search Advertising. Journal of Marketing Research, forthcoming. Shaked, A. and J. Sutton. 1982. Relaxing Price Competition through Product Differentiation. Review of Economic Studies, 49(1): 3-13. Shaked, A. and J. Sutton. 1983. Natural Oligopolies. Econometrica, 51(5): 1469-83. Simester, D. 1995. Signalling Price Image Using Advertised Prices. Marketing Science, 14 (2), 166-188. Spence, M. 1973. Job Market Signaling. The Quarterly Journal of Economics, 87 (3), 355-374. Stromberg, D. Mass Media Competition, Political Competition, and Public Policy. Review of Economic Studies, 71(1): 265-284. Varian, H. 2007. Position Auctions. International Journal of Industrial Organization 25 (6) 1163-1178. 105 Vickrey, W. 1961. Counterspeculation, Auctions and Competitive Sealed Tenders. Journal of Finance 16(1) 8-37. Wilbur, K., Y. Zhu. 2009. Click Fraud. Marketing Science. 28(2). Xiang, Y. and M. Sarvary. 2007. News Consumption and Media Bias. Marketing Science, 26(5): 611-628. Xu, L., J. Chen., A. B. Whinston. 2009. To Place Better or Price Cheaper? Bidding and Pricing under Keyword Advertising. Working paper, University of Texas at Austin. Yao, S., C. F. Mela. 2009. A Dynamic Model of Sponsored Search Advertising. Unpublished manuscript, Duke. http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1285775. Yaveroglu, I., N. Donthu. 2008. Advertising Repetition and Placement Issues in Online Environments. Journal of Advertising. 37(2) 31-43. Yildirim, T. P., E. Gal-Or and T. Geylani. 2011. User Generated Content on News Media. Working Paper, University of Pittsburgh. 106 APPENDICES Appendix A Lemma 1. The dominant strategy for any direct response advertiser under BPE is to choose a high effort level. Proof: When direct response advertiser i gets slot k in period t with a CPC bid, its profit is kt E it it Di it k c ikt C r X       . This is weakly increasing in it x so long as E it k kt Di X C r   , which must be true if the advertiser bid rationally and won the auction. If the direct response advertiser enters a CPM bid, its profit is kt Di it k m ikt C r X     , which is strictly increasing in it x . Intertemporal profit maximization also favors high effort. If the direct response advertiser enters a CPM bid in period 1  t , then BPE ensures that costless effort in period t does not affect profits in period 1  t . If i enters a CPC bid in period 1  t , its profits are strictly lower since i E it    1 So low effort in period t wouldn’t increase its profit in period 1  t by the arguments in the previous paragraph. Q.E.D. Lemma 2. Any brand advertiser entering a CPM bid under BPE is indifferent between high effort and low effort. A brand advertiser entering a CPC bid will exert low effort. Proof: We begin with the first statement. The brand advertiser’s current-period revenues ikt R are not a function of its costless effort level it x . When it enters a CPM bid, its current costs also are not a function of its effort level it x . Since it has used a CPM bid, BPE ensures that the 107 gatekeeper will always expect it to choose low effort; therefore, none of its future profits can be impacted by its current effort level. Since current and future profits are unaffected by effort, the advertiser is indifferent between high and low effort. Now we consider the second statement. When a brand advertiser submits a CPC bid in period t, its one-period incentive is to minimize its click-through rate in order to minimize its advertising cost. And the publisher’s BPE expectation function ensures that there is no effect of it x on advertiser payoffs in future periods. The advertiser’s use of a CPC bid in period t leads the publisher to set low click expectations in all future periods regardless of the effort entered in period t. Q.E.D. Lemma 3. Under BPE, direct response advertisers always enter CPM bids. Brand advertisers are always indifferent between the best possible CPM bid and the best possible CPC bid. Proof: Beginning with the first claim, we show that any direct response advertiser i has a strict preference for a CPM bid in period 0 and then show that it never switches bid types. From Lemma 1, we know that direct response advertisers will exert high effort regardless of bid type choice. Since i E i    0 under BPE, if direct response advertiser i gets slot k in period 0, its profit from a CPC bid is           E i k Di i k c ik C r X 0 0 0 0    , strictly less than its CPM bid profit of 0 0 0 k Di i k m ik C r X     , leading to the preference for CPM bidding in period 0. Given a CPM bid in period 0, direct response advertiser i faces i i E i      1 in period 1. It gets 1 1 1 k Di i k m ik C r X     with a CPM bid, or           i k Di i k c ik C r X    1 1 1 with a CPC bid in period 108 1. Profits are strictly higher with a CPM bid. We can iterate forward to show that CPM bidding dominates CPC bidding in every period of the game. Now suppose advertiser i is a brand advertiser. Under BPE, its first-period profit is either 0 0 k Bi k m ik C r Y    with a CPM bid or 0 0 0 0 k E i i Bi k c ik C r Y      with a CPC bid. c ik 0  is decreasing with effort and, conditional on low effort, we have c ik m ik 0 0    . BPE ensures that the brand advertiser will continue to face i E it    in subsequent periods and will therefore maintain its indifference between bid types. Q.E.D. Proposition 1. At least one equilibrium exists. In any equilibrium, the publisher uses BPE and advertisers behave in accordance with Lemmas 1-3. Proof: We first prove equilibrium existence by addressing each point in Definition 1, then show BPE is the unique equilibrium belief by contradiction. 1. IC constraint. Lemmas 1, 2, and 3 describe the optimal strategy of brand and direct response strategy, which maximizes their profit under BPE and satisfies the IC constraint. 2. IR constraint. Assumption 2 states that each advertiser is charged the minimum amount necessary to keep its place in the ranking, which guarantees that advertisers get non-negative profits in equilibrium. 3. Publisher rationality. We prove this by contradiction. If the publisher’s expectation is ] , ( ) (          i i s it it E it c g , straightforward extensions to Lemmas 1-3 will show that the dominant strategy for brand advertisers is to submit a CPC bid with low effort, and for direct response advertisers it is to submit a CPM bid with high effort. Assume that, under BPE, brand 109 advertiser i gets position k with a CPM bid * m it b . Under our supposed expectation function, i’s optimal bid is ) ( * * c g X b Y b s it it E it k m it k c it      . Holding other advertisers’ bids constant, i gets slot k and pays k E it i C   . So, the publisher’s revenue loss is 0 ) 1 (   k E it i C   . Every direct response advertiser gets an identical payoff if we change BPE, so the switch in publisher expectations does not alter direct response advertisers’ equilibrium bids or publisher revenues from those bids. So, any deviation from BPE will reduce publisher revenues from brand advertisers, and no deviation can increase publisher revenues from direct response advertisers. This completes our proof that BPE maximizes publisher revenues. 4. Consistency of Publisher Beliefs. Under BPE, the strategy profile for direct response advertisers is to submit CPM bids with high effort; and brand advertisers get the same payoff with CPC bids with low effort or CPM bids with any effort. The publisher’s belief about advertiser i in time period t is given by Bayes’ rule, ) | , Pr( ) | , Pr( ) | , Pr( ) , | Pr(                it i it it i i it it i i it it i i E it H H H H          . Advertisers can be divided into two groups: those that submit at least one CPC bid, and those that do not. For this first group, BPE specifies i E it    forever. First, from the advertiser’s strategy profile, we know advertiser i is a Brand advertiser. Second, advertiser inertia removes the possibility that i randomly changes effort across period since BPE has removed the profitability of doing that. Therefore 0 ) | , Pr(        it i i it H and 0 ) | , Pr( ) | , Pr( ) | , Pr( ) , | Pr(                          it i it it i i it it i i it it i i E it H H H H , proving consistency of BPE publisher beliefs. For the other group of advertisers, there are two cases. Case (1), 110 advertiser i is a direct response advertiser. In this case, i always submits a CPM bid with a high click through rate in time period t-1 i i it      1 , from Lemmas 1 and 3 .Then 1 ) | , Pr(        it i i it H and 1 ) , | Pr(    it i i E it H     , proving consistency. In case (2), i is a brand advertiser. Suppose advertiser i used high effort in period t-1 and i i it      1 . By advertiser inertia, it will put the same effort level in period t, so again we have 1 ) , | Pr(    it i i E it H     . If i instead used low effort in period t-1, the same logic can be used to show consistency of publisher beliefs. This completes the proof that BPE satisfies condition 4. It remains to be shown that there is no other equilibrium belief. We do this by checking deviations from each part of BPE. We first check whether there exists any belief that is different from ] , 0 [ any for , ) ( t s c g i s it it E it        . Suppose ] , ( ) (          i i s it it E it c g . Point 3 above shows this would violate publisher rationality, so any equilibrium belief must contain ] , 0 [ any for , ) ( t s c g i s it it E it        . Second, we check whether there exists any belief that is different from 1  it  if ] , 0 [ every for t s c g s it    . If advertiser i is a direct response advertiser, then we know from Lemma 1 that t i it    ,    . Therefore any deviation 1   it E it   violates consistency of publisher beliefs. Having ruled out any alternate bid-type-contingent beliefs, we complete the consideration of any alternate belief function by looking at beliefs that are not contingent on bid types. The only possible equilibrium belief that is independent of bid type and maximizes publisher revenue is ] , 0 [ , T t i E it      . However, under this belief, the strategy profile for direct response advertisers is to choose to submit a CPM bid and put a high effort. This gives 1 ) | , Pr(        it i i it H and 1 ) , | Pr(    it i i E it H     , so this belief violates Bayes’ rule. Q.E.D. 111 Proposition 2. Under BPE, any repeated GSP equilibrium assignment of advertisers to slots can also be supported in a repeated hybrid advertising auction game. Proof: First we need to discuss, briefly, the repeated GSP auction equilibrium definition. The conditions in Definition 1 also define the GSP equilibrium, though advertisers have only one bid type (CPC). Now we prove the claim. Assume there is a set of CPC bids T t c t b ,..., 1 ) (  for every advertiser i and every time t that constructs equilibrium in a GSP auction. We need to prove that giving advertisers the option to use CPM bidding does not violate any of the conditions in definition 1. By Lemma 3, brand advertisers are indifferent between the best possible CPC bid and the best possible CPM bid. Therefore, brand advertisers would have no incentive to change their bids from CPC to CPM. By Lemma 3, direct response advertisers strictly prefer CPM bidding with high effort in all periods in the hybrid advertising auction. If direct response advertiser i gets slot k in period t with CPC bid c it b in the GSP auction, it can choose a CPM bid which yields an equivalent total willingness to pay in the hybrid advertising auction: c it i i k k m it b Y X b ) (     . If all direct response advertisers follow this strategy, then all advertisers will be allocated to the same slots in the hybrid advertising auction as they were in the repeated GSP auction. Q.E.D. 112 Proposition 3. Under the Uniform Value Depletion Condition, the payment scheme in Definition 3 produces a unique equilibrium with truthful advertiser bids and the VCG allocation of advertisers to slots. Proof: An advertiser may have two reasons to bid untruthfully: to change its equilibrium slot assignment and/or to change its payment. Notice that the payment scheme in Definition 1 ensures that every advertiser’s payment is unrelated to its bid, removing the motivation to change a payment. Further, if a truthful bid would place the advertiser in its most preferred slot, then uncertainty about other advertisers’ private valuations ensures that it will bid exactly its valuation; misreporting risks being allocated to a suboptimal slot without any cost reduction. Therefore, we only need to show that bidding truthfully places each advertiser in its most profitable advertising slot. We start by supposing direct response advertiser i enters a truthful CPC bid Di c it r b  , then show it has no incentive to deviate. Suppose i is assigned to slot k in equilibrium. Suppose it considers raising its bid to get a lower slot k k  ' . Its profit would be ) ( ' ' ' c t ik Di it k c t ik p r X     . Suppose i compared this option to an adjacent slot 1 '  k , which yields ) ( 1 ' 1 ' 1 ' c t ik Di it k c t ik p r X        . Taking the difference between these profits c t ik c t ik ' 1 '     and substituting in for the per-click payments, we find                ) ( 1 ) ( ' ' 1 ' 1 ' ' 1 ' ' 1 ' c t ik E it k c t ik E it k E it Di k k it c t ik c t ik p X p X r X X                             m g k' X b Y X X c g k' b X X p X p X t k k m k k k k t k c t k E t k k k c t ik E it k c t ik E it k 1 ' 1 ' ' 1 ' 1 ' 1 ' 1 ' ' 1 ' ' ' 1 ' 1 ' set 1 slot in advertiser the if ) ( set 1 slot in advertiser the if ) (    113                          m g k' X b Y r X X c g k' b r X X t k E it k M t k k Di k k it t k E it C t k E t k Di k k it c t ik c t ik 1 ' 1 ' ' 1 ' 1 ' 1 ' 1 ' ' 1 ' ' 1 ' set 1 slot in advertiser the if ), )( ( set 1 slot in advertiser the if ), )( (        . We know ' 1 ' k k X X   , so we will have c t ik c t ik ' 1 '     if and only if the second term in parentheses in the previous equation is negative. We also know k k  ' and k k  1 ' . Truthful bidding and Assumption 1 (assignment of advertisers to slots in order of expected total payment) therefore imply that               m g b Y c g b X b X r X t k m t k k t k c t k E t k k c it E it k Di E it k 1 ' 1 ' 1 ' 1 ' 1 ' if if    . (A1) Rearranging terms in (A1) shows that it must be the case that c t ik c t ik ' 1 '     . Since this holds for all k k  ' , we can do this comparison recursively to show the advertiser does not prefer any slot k k  ' . Now suppose advertiser i considers lowering its bid to get a higher slot k k  ' . We compare the profit when the advertiser gets slot 1 '  k with slot ' k . We can show that                          m g k' X b Y r X X c g k' b r X X t k E it k M t k k Di k k it t k E it C t k E t k Di k k it c t ik c t ik 1 ' 1 ' ' 1 ' 1 ' 1 ' 1 ' ' 1 ' ' 1 ' entered 1 slot in adv. if ), )( ( entered 1 slot in adv. if ), )( (        . Similar to above, this implies c t ik c t ik ' 1 '     , which, when applied recursively, indicates that advertiser i is strictly worse off in any slot k k  ' . If direct response advertiser i considers submitting a CPM bid to get slot k k  ' ,                        ) )( ( ) )( ( ) ( ) ( 1 ' ' 1 ' 1 ' 1 ' ' 1 ' ' 1 ' ' 1 ' ' 1 ' m t k Di it k k k C t k E t k k Di it k k m t ik m t ik Di it k k m t ik m t ik b r X X Y b X r X X p p r X X       114 We know that 0 ' 1 '    m t ik m t ik   since                 m g k' b Y c g k' b X b Y r Y t k m t k k t k C t k E t k k m it k Di it k 1 ' 1 ' 1 ' 1 ' 1 ' set 1 slot in advertiser the if , set 1 slot in advertiser the if ,   Applied recursively, this indicates that the advertiser does no better in any slot k k  ' . A similar analysis shows that a CPM bid for any lower slot k k  ' also decreases profits. Now consider what happens when brand advertiser i enters a CPC bid to get slot k k  ' .                              m g k' X b Y X X r Y Y c g k' b X X r Y Y t k k m k k E it it k k Bi k k t k c t k E t k E it it k k Bi k k c t ik c t ik 1 ' 1 ' ' 1 ' ' 1 ' 1 ' 1 ' 1 ' ' 1 ' ' 1 ' ' 1 ' set 1 slot in advertiser the if , ) ( ) ( set 1 slot in advertiser the if , ) ( ) (        and we know that                m g k' b Y c g k' b X r X t k m k k t k c t k E t k k it Bi E it k 1 ' 1 ' 1 ' 1 ' 1 ' set 1 slot in advertiser the if , set 1 slot in advertiser the if ,    . Since k k  ' , we again can deduce that c t ik c t ik ' 1 '     for any k k  ' . The structure of the proof when brand advertiser i submits a CPM bid to get a lower slot k k  ' , submits a CPC bid to get a higher slot k k  ' , or submits a CPC bid to get a lower slot k k  ' is similar and therefore omitted. Next we show advertiser i in slot ] , 1 [ K k  will have non-negative profits. Assume advertiser i is a direct response advertiser with Di r profit per click, truthful bid       m g r c g r b it Di it it Di g it it if if  , and profit         m ikt Di i k c ikt i k Di i k g ikt p r X p X r X it     . If i submits a CPC bid, then                                 K k k K k k k k E i M k k k k k k C k E i E k k k k Di i k c ikt m g I X b Y X X X c g I b X X X r X ' ' 1 ' 1 ' 1 ' ' 1 ' 1 ' 1 ' 1 ' ' ) ( ) ( ) ( ) (      . 115 Since ] , [ ' K k k  , we know that              m g b Y c g b X b X k m k k k c k E k k c i E i k 1 ' 1 ' 1 ' 1 ' 1 ' if if   . So                                                  K k k c i k k k K k k K k k k c i k k k k c i k k k K k k K k k k k E i c i E i k k k k k c i E i E i k k k K k k K k k k k E i M k k k k k k c k E i E k k k k b X X X m g I b X X X c g I b X X X m g I X b X X X X c g I b X X X m g I X b Y X X X c g I b X X X ' 1 ' ' ' ' 1 ' 1 ' ' 1 ' 1 ' ' ' ' 1 ' 1 ' ' 1 ' 1 ' ' ' ' 1 ' 1 ' 1 ' ' 1 ' 1 ' 1 ' 1 ' ' ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) (        ) 1 ( 1 k K c i X X b    . Therefore,                          K k k K k k k k E i M k k k k k k c k E i E k k k k Di m g I X b Y X X X c g I b X X X r ' ' 1 ' 1 ' 1 ' ' 1 ' 1 ' 1 ' 1 ' ' ) ( ) ( ) ( ) (    ) 1 ( 1 k K c i Di X X b r     , implying 0  c ikt  since 0 1   K X and c i Di b r  . If i submits a CPM bid,                         K i k K i k t k M k k k t k k C k E k k k k Di i k m ikt m g I b X X c g I Y b X X X r X ) ( ) ( ) ( ) ( 1 ' 1 ' 1 ' ' 1 ' 1 ' 1 ' 1 ' '    which increases with i  , so the optimal click-through rate is E i i i i        . Since ] , [ ' K k k  , we know that              m g b Y c g b X b Y k m k k k c k E k k m i k 1 ' 1 ' 1 ' 1 ' 1 ' if if  , and . ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( 1 1 ' ' 1 ' 1 ' ' 1 ' 1 ' ' 1 ' 1 ' 1 ' ' 1 ' 1 ' 1 ' 1 ' ' Di i k m k K k K i k m k k k K i k K i k t k m i k k t k k m i k k k K i k K i k t k m k k k t k k m k E k k k k r X b X X b X X m g I b X X c g I Y b Y X X m g I b X X c g I Y b X X X                                          116 Therefore, 0      Di i k Di i k m ikt Di i k m ikt r X r X p r X     . The proof that a brand advertiser would get non-negative profits is similar. We have shown that truth-telling is strictly dominant conditional on advertisers being ranked in order of their total willingness to pay per slot, and that advertisers would rationally participate in the auction. We now use a contradiction to prove that this is the only possible equilibrium. Suppose there is an equilibrium in which advertiser i in slot k had a higher willingness to pay than advertiser i' in slot k k  ' . By the arguments presented above, this would imply it it g ikt g t ik    ' , so i would be strictly better off if it increases its bid until it wins slot k'. Therefore we have found our contradiction and this must not be an equilibrium. Q.E.D. Proposition 4. Under the Uniform Value Depletion Condition, no other truth-telling payment scheme produces higher revenues. Proof: We prove this by contradiction. Below we use the following property of our payment scheme implied by Definition 3:                       m g k X b Y X X c g k b X X p X p X t k k m t k k k k t k c t k E t k k k c ikt E it k c t ik E it k 1 1 1 1 1 1 1 1 1 set 1 slot in advertiser if , ) ( set 1 slot in advertiser if , ) (    . (A2) Suppose there is a payment scheme in a truth-telling mechanism that defines it g ikt q as the price advertiser i pays when allocated to slot k in time t given bid type it g . Assume that direct response advertiser i enters a CPC bid to get slot k in period t. In equilibrium, it must be the case that i is weakly more profitable in slot k than in slot 1  k . This implies Di E it k k c t ik E it k c ikt E it k r X X q X q X    ) ( 1 1 1       . (A3) 117 The right-hand side of (A3) is minimized if we take the smallest value of Di r that preserves the same assignment of advertisers to slots.                      m g k X b Y c g k b r t k k E t k m t k k t k E t k c t k E t k Di 1 1 1 1 1 1 1 set 1 slot in advertiser the if , set 1 slot in advertiser the if ,      . (A4) This value of Di r guarantees i appears in position k if 0   and Di c it r b  (which is implied by the assumed mechanism producing truth-telling in equilibrium). Substituting (A4) into (A3) and taking the limit as epsilon approaches zero, we have c t ik E it k c ikt E it k t k E it k m t k k k k t k E it c t k E t k k k c t ik E it k C ikt E it k p X p X m g k X b Y X X c g k b X X q X q X 1 1 1 1 1 1 1 1 1 1 1 set 1 slot in advertiser the if , ) )( ( set 1 slot in advertiser the if , ) )( (                                      (A5) where the last equality comes from applying (A2). Since it must be that 0 1   K p and 0 1   K q , (A5) implies ] , 1 [ , K k p q c ikt c ikt    . We have shown that no VCG payment scheme can produce higher payments at any slot than our proposed mechanism when a direct response advertiser uses a CPC bid. The structure of the proof when direct response advertiser i submits a CPM bid, when brand advertiser i submits a CPM bid, and when brand advertiser i submits a CPC bid is very similar and therefore omitted. Q.E.D. Proposition 5. If the Uniform Value Depletion Condition fails to hold for some slot k, no payment scheme will always achieve the VCG assignment of advertisers to slots. 118 Proof: We prove this by contradiction. To simplify the proof, we assume 1 1      k k k k Y Y X X for some slot k, but the same arguments presented here will apply if this inequality is reversed. Assume there exists a payment scheme that achieves the VCG assignment. Assume this payment scheme defines it g kt q as the per-exposure payment of any advertiser in slot k in period t. Suppose brand advertiser i with value per exposure Bi r occupies slot k in equilibrium. Since the assumed mechanism yields the VCG assignment, it must have equilibrium truth-telling so Bi m ikt r b  . A condition of equilibrium is that i is assigned to its most-preferred slot, so we have m t k m kt Bi k k q q r Y Y 1 1 ) (      . Now suppose we replace brand advertiser i with a direct response advertiser j with a value per click jt Bi Dj r r   and expected click through rate E jt  . If j enters a truthful CPM bid, it must be the case that m it Bi Dj jt m jt b r r b     and advertiser j is assigned to slot k. However, for ) ) ( ) ( , ) ( ) ( ( 1 1 1 1          k k jt m t k m kt k k jt m t k m kt Dj X X q q Y Y q q r   , this assignment would be unprofitable since we have m t k m kt Dj jt k k q q r X X 1 1 ) (       . (A6) Therefore the presumed mechanism will not always induce direct response advertisers to enter truthful CPM bids. Next we consider what happens if j submits a truthful CPC bid Dj c jt r b  . Suppose we have a brand advertiser i' in slot 1  k with value per impression 119              ) , min( , ) ( ) ( 1 1 ' Dj jt k Dj jt k k k m t k m kt Bi r Y r X Y Y q q r   , jt t i    ' and E jt E t i    ' . Given truthful bidding and a VCG assignment of advertisers to slots, it must be that                 m g k b Y c g k b X b X r X t k m t k k t k c t k E t k k c jt E jt k Dj E jt k 1 1 1 1 1 set 1 slot in advertiser the if , set 1 slot in advertiser the if ,    which guarantees advertiser j gets slot k with bid c jt b . This requirement is easily satisfied since we have not placed restrictions on k X and k Y . k Y . For example, it is strictly satisfied if jt E jt    and k k Y X  . j's revealed preference implies ) ( ) ( 1 1 1 c t k k c kt k jt Dj jt k k q X p X r X X         . (A7) Combining (A6) and (A7), we have the following inequality: m t k m kt Dj jt k k c t k k c kt k jt q q r X X q X q X 1 1 1 1 ) ( ) (            which simplifies to m t k m kt c k k c k k jt q q q X q X 1 1 1 ) (        . (A8) Advertiser ' i should be put lower than advertiser j if we have a truthful mechanism. However, Advertiser ' i cannot submit a CPM bid with a bid ' ' Bi m t i r b  to get slot 1  k since m t k m kt Bi k k q q r Y Y 1 ' 1 ) (      . Advertiser ' i has incentive to increase its bid and get slot k. The only way to preserve the truth-telling property of our assumed mechanism is to assume advertiser ' i submits a truthful CPC bid t i Bi c t i r b ' ' '   and gets slot 1  k . This implies that the following condition has to be satisfied: ) ( ) ( ) ( 1 1 1 1 ' ' 1 c t k k c kt k j C k k c ikt k i Bi k k q X q X q X q X r Y Y             Together, we have 120 ) ( ) ( 1 1 ' 1 1 c t k k c kt k j Bi k k m t k m kt q X q X r Y Y q q           . This gives us an inequality ) ( 1 1 1 c t k k c kt k j m t k m kt q X q X q q        which directly contradicts inequality (A8). Therefore we have proven that our assumed VCG mechanism cannot exist. Q.E.D. Appendix B Here we show how advertisers behave under the payment scheme described in Definition 3. For this appendix only, we assume k X Y k k   , since, in the absence of random clicks, an ad exposure is necessary but not sufficient for an ad click. Proposition B1. Under BPE and the payment scheme in Definition 3, all advertisers submit CPM bids. All direct response advertisers exert high effort while brand advertisers are indifferent between low effort and high effort. Proof: To show CPM bidding dominates, we calculate the difference in total payments between the two bid types for advertiser i in slot k in period t:                     K i k K i k t k m t k k k k k t k c t k E t k k k k k m ikt c ikt E it k m g I b X Y X X c g I b Y X X X p p X ' ' 1 ' 1 ' 1 ' ' 1 ' 1 ' 1 ' 1 ' ' ) ( ) 1 )( ( ) ( ) 1 )( (   Since k k X Y  for all k, so 0 1   k k X Y and 0 1   k k Y X . Therefore ( 0   m ikt c ikt E it k p p X  so advertisers always prefer CPM bidding. 121 The results regarding effort follow directly from the proofs of Lemmas 1 and 2, which can be directly applied under the new payment scheme. Q.E.D. Appendix C In this section we consider a nonrational publisher whose click-through expectations are only set as a function of past click-through rates, rather than considering current or past bid types. Definition C1 describes our publisher’s expectations. Definition C1: Historical Publisher Expectations (HPE) are based on click-through rates in the previous  periods: ) ,..., ( 1 0   it i it E it G    with the properties (i) a EG it i it   ) ,..., ( 1 0   if and only if t s a s it      0 ,  ,and (ii) 0    s it t G  for all . HPE incorporate the intuitive properties that publisher expectations are degenerate if and only if an advertiser has never changed its costless effort level and expected click-through rates are nondecreasing in advertisers’ past click-through rates. This allows for a wide range of expectation functions, including weighted averages and stochastic functions. We characterize our notion of equilibrium in Definition C2. Note that, since we now consider a nonstrategic publisher, we require a different equilibrium concept. Definition C2: A Subgame Perfect Nash Equilibrium (SPNE) is defined by any set of bids T t t b ,..., 1 ) (  and any set of costless effort levels T t t x ,..., 1 ) (  for which the following conditions hold: ) ,..., 1 , 0 ( t s  122 1. Incentive Compatibility: the choice sequence of effort levels ( iT i x x , , 1 ) and bids ( iT i g iT g i b b , , 1 1 ) maximize expected profits a i  E for all advertisers i=1,…,N. 2. Advertiser Rationality: for any advertiser i who wins slot k in period t, 0 E  it g ikt  . The difference between definition C2 and definition 1 is that here the publisher is not required to set click-through expectations to maximize its long-run profits, essentially modeling it as a nonstrategic player. We define a “bid reversal” as an advertiser using a CPM bid with high effort in period t, followed by a CPC bid with low effort in period 1  t . We begin by showing that Historical Publisher Expectations lead to strategic bid reversals in equilibrium. Proposition C1: Under HPE, every brand advertiser engages in at least one bid reversal. Proof: First, we show that T consecutive CPM bids would be suboptimal. If brand advertiser i uses pure CPM bidding, it can costlessly exert high effort in at least one period prior to t, so t EG E i it i t E it     , ) ,..., ( 1 0     . Its expected payoff is .... ) ( ) ( ) ( ) ( 2 2 1               k ik k ik k ik ikt ikt ikt ikt C R C R C R E E      However, if i exerts high effort in any period prior to period t and uses a CPC bid in period t with low effort, then its expected payoff is ... ) ( ) ( ) ( 2          kt ikt kt ikt kt it i ikt ikt C R C R C EG R E    , which is strictly higher than . So T consecutive CPM bids cannot be optimal. ikt E  123 Second we show T consecutive CPC bids would also be suboptimal. Assume that brand advertiser i exerts low effort in every period, t i E it   ,   . Its expected payoff is .... ) ( ) ( ) ( ) ( 2 2 1               kt ikt kt ikt kt ikt ikt ikt ikt ikt C R C R C R E E       . If the advertiser submits a CPM bid with a high effort at time t, then ... ) ( ) ( ) ( ) ( 2 2 1 ' 2 ' 1 ' '                 kt E it i ikt kt E it i ikt kt ikt ikt ikt ikt ikt C R E C R E C R E E           . We know that q G G G i i i i q it i i i i q it q it it it i q it E q it             ) ,..., , ,..., ( ) ,..., , ,..., ( ) ,..., , ,..., ( 1 1 0               so q E q it i    1   . is strictly higher than , indicating that T consecutive CPC bids would be suboptimal for any brand advertiser. Thus any brand advertiser must use at least one bid reversal in equilibrium. Q.E.D. Proposition C1 establishes that, under HPE, brand advertisers will strictly prefer a mix of CPC bidding and CPM bidding over time. Could it be the case that every brand advertiser is incented to make just one bid reversal over the course of the game, yielding minimal harm to publisher revenues? We now make it clear that bid reversals can be employed with maximally high frequencies under some conditions. We first define the set of strategies the advertiser would follow and then show that members of this set may be used in equilibrium under HPE. Definition C3: A Lattice Strategy is a repeated strategy profile in which an advertiser submits a CPM bid with a high effort level in some periods and enters an equivalent CPC bid with a low effort level in other periods. ' ikt E  ikt E  124 A Lattice Strategy is a tactic in which a brand advertiser repeatedly manipulates the publisher’s historical expectations. It uses CPM bidding with a high click-through rate to calibrate a higher expected click-through rate in future periods. It later profits from this heightened click-through expectation by switching to CPC bidding with low effort to reduce its advertising costs. To show the Lattice Strategy may be played in equilibrium, we employ the One-Stage Deviation Principle of Blackwell (1965), a method of testing whether a sequential strategy profile in a dynamic game is subgame perfect. This principle states that a multi-stage strategy is subgame perfect in a dynamic game if and only if no player has incentive to deviate from this strategy profile in exactly one stage. Fudenberg and Tirole (1991) provide a detailed discussion. This substantially simplifies the process of showing a strategy is subgame perfect since it is not necessary to rule out deviations in every single stage of the game. An infinite number of Lattice Strategies exist. We consider here a Two-Stage Lattice Strategy in which a brand advertiser uses CPM and CPC bids in alternating periods. Besides being simple relative to some other Lattice Strategies, the Two-Stage Lattice Strategy would lead to the most frequent bid reversals. This shows that strategic bid reversals could occur with high frequency. To simplify the proof of Proposition C2, we assume a particular form of HPE in which the publisher sets click-through expectations stochastically according to each advertiser’s observed click-through rates in the previous  periods. That is, we assume         it i it i i E it       1 y probabilit with y probabilit with , where         1 1 s s it it x for t   , or      t s s it it x t 1 1  for t   . 125 We also assume, for simplicity, that the assignment of advertisers to slots remains constant over periods t. Proposition C2: When 2 1 2 1 2 1 1 2 1 1 1                   , a SPNE may exist in which all brand advertisers employ the Two-Stage Lattice Strategy under HPE. Proof: Since the Lattice Strategy is a two-stage strategy, by the One-Stage Deviation Principle we can prove it is a SPNE strategy if we can show that i has no incentive to deviate from it in either stage given other advertisers’ actions. We prove that, for advertiser i, the Lattice Strategy strictly dominates other options in the first period (stage t-1). Then, we show that it is also strictly dominant in the second period (t). We assume here that   t for expositional convenience; the arguments are easily applied to smaller t. We start by showing that the Lattice Strategy is strictly dominant for brand advertisers in period t-1. In period t-1, i has three other options: low-effort/CPM bid, high-effort/CPC bid, or low-effort/CPC bid. Low effort with a CPM bid would leave i’s payoff in period t-1 unchanged, but expected profits in period t are decreasing in 1  it  . We can also quickly rule out a high-effort/ CPC bid as this payoff is strictly dominated by a high-effort/CPM bid. The final possible deviation in period t-1 is switching to a CPC bid with low effort, which would yield kt E it it ik c ikt C R 1 1 1         . i's total payoff from the switch would be . ] 1 2 / ) ( 1 2 / ) [( ) ( ] 1 2 / ) ( 1 2 / ) [( ] 2 1 ) ( 2 1 ) [( ) ( 3 2 ' 1 ' ' 1 ' 1                                                      k i i i ik k ik k ik k i i i ik k ik k i i i ik k ik ikt ikt ikt ikt C R C R C R C R C R C R C R E E 126 i's total payoff from not switching at period t-1 is: ) ( 1 1 1         ikt ikt ikt ikt E E    ] 2 1 ) ( 2 1 ) [( ) ( k i i i ik k ik k ik C R C R C R            . ] 2 1 ) ( 2 1 ) [( ) ( 3 2         k i i i ik k ik k ik C R C R C R      i has no incentive to deviate from the Lattice Strategy in period t-1 if and only if 0 ' 1 1       ikt ikt E E . k i i i k i i i k i i i k i i i ikt ikt C C C C E E ) ( ) ( ) ( 2 1 1 3 ' 1 1                                    ) 1 1 2 1 ( )] ( 1 2 1 [ 2 1 1 3                                k i i i k i i i C C . Thus, if 2 1 1 1 2 1          , the Lattice Strategy is strictly dominant in period t-1. In period t, i can again deviate by choosing a high-effort/CPC bid, low-effort CPM bid, or high- effort CPM bid. We can quickly rule out these first two options because the low-effort/CPC bid dominates both the high-effort/CPC bid and low-effort/CPM bid options. The main question is whether the deviation to the high-effort/CPM-bid option is profitable. In this case its total expected payoff in period t is ) ( ' 2 ' 1 ' '         ikt ikt ikt ikt E E    . ] 1 2 / ) ( 1 2 / ) [( ) ( ) ( 2                       k i i i ik k ik k ik k ik C R C R C R C R The expected payoff if the advertiser doesn’t deviate at period t is: 127 ) ( 2 1        ikt ikt ikt ikt E E    ) ( ] 2 1 ) ( 2 1 ) [( k ik k i i i ik k ik C R C R C R                    ] 1 2 / ) ( 1 2 / ) [( 2         k i i i ik k ik C R C R . The difference in payoff is ' ikt ikt it E E      k i i i k i i i k i i i k i i i C C C C ) ( , , ) ( ) ( 2 1 4 2                             ) 1 1 2 1 ( )] ( 1 2 1 [ 2 1 2 4 2                             k i i i k i i i C C So if 2 1 1 1 2 1          and 2 1 1 1 2 1 2          , the Lattice Strategy is strictly dominant in period t. Q.E.D. Essentially, the Lattice Strategy involves an investment behavior and a payoff behavior. The investment takes place in the periods in which the brand advertiser enters a CPM bid with a high effort level. The payoff occurs in the periods when the advertiser uses a CPC bid with a low costless effort level. The conditions needed for SPNE existence require that 1) the net present value of future investment returns are high enough to prevent the advertiser from taking payoffs during investment periods; and 2) that current-period payoff incentives are high enough that the advertiser does not optimally invest during payoff periods. More sophisticated Lattice Strategies can also be analyzed, such as “bid CPM with high effort for w periods, followed by CPC with low effort for y periods,” or “draw a binomial random variable w with probability p, and play CPM with high effort whenever w=1; play CPC 128 with low effort when w=0.” The parameter space in which a Lattice Strategy may be played in equilibrium increases in the length of the number of periods of CPM bidding included in the strategy. The profitability of all Lattice Strategies can be eliminated by BPE. Appendix D Proof of Lemma 1. Assume there exists a fully informative equilibrium with a one-to-one stance mapping ] 1 , 0 [ ] 1 , 0 [ : *  s between s and t. We establish a contradiction in two steps: we first show that if a fully informative equilibrium exists, then for ] , 0 [ 2 1  t , the equilibrium media stance ] , [ ) ( 2 1 * t t s  . (Similarly, if ] 1 , [ 2 1  t , ] , [ ) ( 2 1 * t t s  ). Second we show these conditions provide a unique optimal choice of media stance regardless the value of t, which means that consumers cannot update their beliefs fully informatively. Step 1. Fix ] , 0 [ 2 1 1  t and denote ) ( 1 * 1 t s s  . We first establish the following fact. For any 1 2 t t  , we must have ) | ( ) | ( 1 2 1 1 s t s t    . Suppose otherwise. Then the media could report either 1 s or 1 2 * ) ( s t s  and earn equilibrium payoffs. Consumers could not, therefore, update their beliefs fully informatively. Using this condition, we show that 1 s lies in ] , [ 2 1 1 t . First observe that if 1 1 t s  then 2 1 1  s . To see this, take some state of the world 1 2 s t  . Profits at these states of the world with a stance 1 s are expressed: } ) ( , ) 1 max{( ) | ( 2 1 2 1 1 1 1 1 z s z s d s t M V s t        ; and } ) ( , ) 1 max{( 1 1 ) | ( 2 1 2 1 1 2 1 2 z s z s d s t M V s t          129 The condition ) | ( ) | ( 1 2 1 1 s t s t    implies that 1 2 1 1 1 1 s t s t    , or 1 1 2 1 1 1 t t s s    . Given that ] 1 , [ 1 2 s t  we have 1 1 1 1   s s , or 2 1 1  s . We now show that 1 1 t s  . For some 1 2 s t  , the profit expressions above and the condition ) | ( ) | ( 1 2 1 1 s t s t    imply that 1 1 1 2 1 1 s t s t    . But ] , 0 [ 1 2 s t  implies 1 1 1 1 1    s t or 1 1 t s  .A similar argument establishes that ] 1 , [ ) ( 2 1 *  t s whenever ] 1 , [ 2 1  t . Step 2: We show that it is impossible to have a one to one mapping that can satisfy the necessary conditions we specified above. Suppose there is a ) ( ) ( 2 1 1 * 1      t s s which is associated with    2 1 1 t with 0   . From Step 1 we know ] , [ ) ( 2 1 1 1 t s   . We can see 2 1 1 0 lim   t  , therefore 2 1 1 0 ) ( lim     s . That means when 2 1  t the associated media stance   2 1 2 1 *  s under fully informative equilibrium. However, we can see   ) ' | ' ( ) ( | 2 1 2 1 2 1 s t z d M V s t          for all ' t and for all 2 1 '  s That is, for any state of the world, the media’s profit is strictly highest when announcing 2 1 '  s . The monopoly can charge a higher price and earn more profit by not telling the truth of the state. This contradicts the requirement of a fully informative equilibrium within [0,1]. Finally, it follows directly that when 0  d , the medium has no incentive to distort the reporting and the only equilibrium is to report t t s  ) ( * , which is fully informative. Q.E.D. Proof of Proposition 1 We show that when 1  x , for any set of dividing points x i i a , , 0 ) (   and media stances x i i s , , 1 ) (   that satisfies (1), (2), and (3), the reporting rule defined in (2) is optimal for the medium’s profit maximization given purchasing rules under (4), and the purchasing rules are optimal for consumers under the reporting rule defined by (1) and (2). 130 For any PBE, we must specify consumers’ out-of-equilibrium beliefs. The most intuitive belief system specifies that when consumers observe a media stance i s s  ' , all i, consumers do not update their knowledge about the state of the world and believe the medium’s reporting is uninformative. Under this out-of-equilibrium belief, the expected number of facts is 2 1 . We show that when 1  x , if a set of dividing points x i i a , , 0 ) (   and media stances x i i s , , 1 ) (   satisfies (1), then the reporting rule defined in (2) is optimal for the medium’s profit given purchasing rules under (4). Suppose ] , [ 1 i i a a t   and let s be any stance in ] , [ 1 i i a a  . Since 0 2 ) 1 )( ( ) 1 ( ) )( ( ) , , ( 3 1 2 3 1 2 1 2 1 2                d s a a a M s a a Ma s a a s i i i i i i i i i  , we know that ) , , ( 1 i i i a a s   is concave in s on the compact set ] , [ 1 i i a a  which guarantees the maximizer in (2) is unique. What’s left is to show consumers decision rule 1 ) (    r is optimal for all consumers when reporting rules and beliefs are specified as (1) to (4). We can see that not buying cannot increase a consumer’s payoff since 0 )] | , , ( [ 1 1  s p s n u E b for all consumers. Last we show if a set of dividing points x i i a , , 0 ) (   and media stances x i i s , , 1 ) (   satisfies (1) and (2), then (3) is satisfied. We know that when 1  i , and x: 2 1 1 1 2 1 1 1 1 ) 1 ( ) 1 ( ) 1 ( 2 2 ) , 0 , ( z s d a s a M a M V a s                2 1 2 1 1 1 ) ( ) 1 ( 2 ) 1 ( 2 ) 1 , , ( z s d a s a M a M V a s x x x x x x x                   We first see if 1 1 1    x a a , then ) , 0 , ( 1 1 a s  and ) 1 , , ( 1  x x a s  are the same function by treating x s  1 as a variable. Hence the optimal choice defined by (2) satisfies 1 1 1    x s s . And it is easy 131 to see that when 1 1 1    x a a and 1 1 1    x s s , ) 1 , , ( ) , 0 , ( 1 1 1   x x a s a s   The structure of the proof for 2 2 1    x a a , 1 2 1    x s s and so on is similar. Q.E.D. Proof of Lemma 2 Based on Proposition 1, when 1  x the set of dividing points are 0 0  a , 1 1  a and 2 1 1  s . It is obvious (3) and (4) of Proposition 1 are satisfied. We want to check whether 2 1 1  s is optimal for the medium under consumers’ expectations. Since a consumer’s expected utility is p b s d V s p s n u E M b      2 1 2 1 1 ) ( )] | , , ( [ , the highest price the media can charge is 2 1 2 ) 1 ( z s d V p M      . Since all consumers purchase at this price, this is also represents the media’s profit. We can directly see that 2 1 1  s maximizes profit and hence this set of dividing points and the media stance satisfies (1) and (2) of Proposition 1. What’s left is to show that consumers’ decision rule 1 ) (    r is optimal for all consumers when reporting rules and beliefs are specified as (1) to (4) of Proposition 1. We can see not buying can lead to lower payoff for consumer since 0 )] | , , ( [ 1 1  s p s n u E b for all consumers. The profit follows immediately from (1) in Proposition 1. We now show there exists a cutoff point 1 M such that when 1 0 M M   , it is impossible to have a partially informative equilibrium. Let x i i a , , 0 ) (   denote a set of diving points, with 2  x as characterized in Proposition 1. Suppose ] , 0 [ 2 1  t and consider any interval ] , 0 [ ] , [ 2 1 1   i i a a . For t in this interval, the optimal stance ] , [ 1 i i a a s   must solve the first-order condition for the maximization in (2) of Proposition 1: 0 ) 1 ( 2 ) 1 ( 2 ) 1 ( 2 ) , , ( 2 2 2 2 1 1 1                     z s d s a s a a a M s a a s i i i i i i  . 132 This has a solution when ) /( ) 1 ( 4 1 2 i i i i a a a a z d M      , a condition which must hold for all intervals ] , 0 [ ] , [ 2 1 1   i i a a . Define )] /( ) 1 ( 4 [ min 1 2 , 1 2 1 1 i i i i a a a a a a z d M i i        , It is immediate that 0 1  M . In fact 1 M is positive except possibly for 0  i a or z a i  1 . But Lemma 1 established that there does not exist a fully informative equilibrium, which implies that that 0  i a . And, 2 1  i a and 2 1  z imply that z a i  1 . Hence, 0 1  M for ] , 0 [ 2 1  t . We now show that when 1 0 M M   , there is no partially informative equilibrium. Based on the first order condition above, for all intervals ] , [ 1 i i a a  lying to left of 2 1 , we have i i a s  . If 2  x then 2 1 2 1   s s , which implies that consumers cannot update about their beliefs about which interval contains the state. Hence, there does not exist a partially informative equilibrium with 2  x . When 3  x , 1 1 a s  when ] , [ 1 0 a a t  means that the number of reportable facts is 2 1 1 ) 1 ( 2 1 1 ] 1 [ 1 2 1 1      s a a n . For the interval ] , [ 2 1 a a since 2 1 1 a a   because of symmetry, the optimal stance 2 1 2  s , which means 2 1 2  n . Therefore, ) , , ( ) , , ( 1 0 1 1 2 1 2 1 2 a a a s a a s      . Finally, when 3  x , 2 1 1  n , which is less than any other i i a a i n 2 2 1 1    when 2 1  i a . Therefore ) , , ( ) , , ( 1 0 1 1 1 a a a s a a a s i i i i       , which violates the requirement of equal profitability across intervals (condition (1) of Proposition 1). Q.E.D. Proof of Proposition 2 We first show when 2 M M  , there exists a partially informative equilibrium with x=2. Define ) ( 2 2 1 2 z d M   . If there are two intervals in equilibrium, then the first order condition of the maximization in (2) of Proposition 1 is 0 ) 1 ( 2 ) 1 ( 2 ) 1 ( ) , 0 , ( 2 1 2 1 1           z s d s a a M s a s  . 133 When 2 M M  , the optimal 2 1 1  s for ] , 0 [ 2 1  t , and 2 1 2  s for ] 1 , [ 2 1  t . It is easy to verify this specified media reporting rules satisfies the requirement of PBE in Proposition 1. Hence we showed that when 2 M M  , there exists a partially informative equilibrium with x=2. Also given the definition of 1 M in the proof of Lemma 2, we know 2 1 M M  . Next we show there exists another cutoff point 2 3 M M  such that when 3 M M  , the media is strictly more profitable in the partially informative reporting than in the uninformative equilibrium. When the monopoly media reports uninformatively, the expected profit is 2 2 1 1 ) ( 2 z d M V      . However, in the partially informative equilibrium with 2  x , 2 1 ) 1 ( 4 2 ) 1 ( 1 s z d M V s M         with ] , 0 [ 2 1 1  s . Notice that if 1 s is an interior solution to the maximization condition of part (2) of Proposition 1, then it must solve ) 1 )( 1 ( 2 ) 1 ( 4 1 1 1 s s z d s M      . This allows us to characterize the condition 1 2    , by the inequality:   2 2 1 1 1 ) ( 2 ) 1 ( 3 ) 1 ( 2 z d z s s z d M        . Since the right-hand side is decreasing in 1 s , a sufficient threshold for 1 2    occurs when 0 1  s . Hence, define ) 3 )( 1 ( 2 3 z z d M    . What’s left is to check is whether 1 2    holds for 3 M M  when 1 s is not an interior solution, but rather a corner solution, to the maximization condition of part (2) of Proposition 1. In that case, we find when ) 1 ( 8 z d M   , 1 s is always equal to 0 and 2 4 3 2 ) 1 ( z d V M      . For the medium to be partially informative, we need ) 4 3 ( z d M   to guarantee 1 2    . But this is automatically satisfied under the condition 134 ) 1 ( 8 z d M   since ) 4 3 ( ) 1 ( 8 z d z d    . Therefore we have shown when 3 M M  , the media prefers partially informative reporting with at least 2 intervals. The fact that 3 2 M M  follows directly from the comparison their definitions. Q.E.D. Proof of Proposition 3 First we can see if both media report truthfully, they will engage into Bertrand competition and obtain zero profit. But if one media deviates, consumers believe both are uninformative and the position differentiation permits a markup for the media. So the deviation is profitable. Therefore a truthful revealing equilibrium is never optimal for both media. To show there doesn’t exist a fully informative equilibrium in duopoly, we followed Lemma 1 in Battaglini (2002) such that no truthful informative equilibrium implies no fully informative equilibrium exists. See Battaglini (2000, 2002) for further details. Q.E.D. Proof of Proposition 4 Proved by contradiction. We analytically show when 12 5  z there does not exist any partially informative equilibrium with two media. When 2 1 12 5   z , it is impossible to analytically prove the non-existence of partially informative reporting equilibrium with two media. We therefore establish this case numerically. Numerical analysis indicates this type of equilibrium is not possible either. Assume there exists a partially informative equilibrium with two media with a set of dividing points x i i a , , 0 ) (   in ] 1 , 0 [ , and a set of media stance choice ] , [ ) , ( 1 , , 1 i i x i B i A i a a s s     , where B i A i s s  . We know given the choice of media stances, consumers first formalize belief about the number of facts A i n and B i n , then make purchase decision based on the price A p and B p . The demand for medium j and k is given by 135 ) 2 1 ( 2 2 ] ) ( ) ( [ z z s s d p p n n M s s D A i B i A B B i A i B i A i A i          and ) 2 1 ( 2 2 ] ) ( ) ( [ 1 z z s s d p p n n M s s D A i B i A B B i A i B i A i k i           . The profit of each medium is A i A i A i p D   and B i B i B i p D   . The respective first order conditions on prices imply: ] ) 6 2 )( ( [ 3 1 M z s s s s d p B i A i A i B i A        ] ) 6 4 )( ( [ 3 1 M s s z s s d p k i j i j i k i B        and with corresponding profits ) 2 1 )( ( 18 ] ) 6 2 )( ( [ 2 z s s d M z s s s s d A i B i B i A i A i B i A i           ) 2 1 )( ( 18 ] ) 6 4 )( ( [ 2 z s s d M s s z s s d A i B i B i A i A i B i B i           where ) ( B i A i n n    . Now consider the first interval ] , 0 [ 1 a , in this interval the expected number of facts ] ) 1 ( ) 1 ( 1 [ 2 1 ) ( ) 1 ( ) 1 ( ) ( 2 1 1 1 1 1 0 1 1 1 1 1 A i a s A s A A s a a dt a t f s t dt a t f s t n A A           , ] ) 1 ( ) 1 ( 1 [ 2 1 2 1 1 1 B i B s a a n     , and ] ) 1 ( 1 ) 1 ( 1 [ 2 ) 1 ( 1 1 1 2 1 A B s s a a       . Therefore 0   if B A s s 1 1  . We can see medium B is at a competitive disadvantage. Therefore we want to check whether medium B has incentive to deviate. Consider the deviation in which medium B “jams” A’s stance by choosing a stance outside the interval ] , 0 [ 1 a . In the assumed equilibrium, we know B earns ) 2 1 )( ( 18 ] ) 6 4 )( ( [ ) 0 , , ( 1 1 2 1 1 1 1 1 1 1 z s s d M s s z s s d s s A B B A A B B A B             , 136 which is obviously larger when 0   . Suppose media B jams A’s stance using the stance 1 ˆ a s B  Then consumers cannot update their belief about the state of the world and expect media have equal number of facts so that 0   . Hence if there exist such a 1 ~ a s B  such that ) 0 , , ( ) 0 , ~ , ( 1 1 1 1 1      B A B B A B s s s s   , then media B can profitably deviate by jamming A. We know when 0   , the optimal stance choice of media B is given by the best response function 0 6 4 ~ 3 1     z s s B A , or ) 6 4 ( ~ 1 3 1 z s s A B    . If 6 3 4 1 a z   , then 1 ~ a s B  for any ] , 0 [ 1 1 a s A  . Under this condition media B has incentive to jam A. In order to determine when this condition is met, we consider the case of ] 1 , [ 1   x a t with B x A x s s  . In this case            A x x x A x s a a n 2 1 1 1 ) 1 ( 2 1 and            k x x x B x s a a n 2 1 1 1 ) 1 ( 2 1 . We can see B x A x n n  so that 0   and ) 0 , , ( ) 0 , , (      B x A x A x B x A x A x s s s s   . In a manner similar to finding B s ~ above, we find a 1 ~   x A a s such that ) 0 , , ~ ( ) 0 , , (      B x A A x B x A x A x s s s s   Maximizing ) 0 , , (   B x A A x s s  over A s implies ) 2 6 ( ~ 3 1    z s s B x A . And under the condition that ) 1 3 ( 1 6 1    x a z , 1 ~   x A a s for any ] 1 , [ 1   x B x a s and jamming is a profitable deviation for A. Together we know that if   6 1 3 6 3 4 1 1 , max     x a a z some media will find jamming a profitable deviation. Since 1 a , the unconditional minimum upper bound for z is when 2 1 1 1    x a a , so that     12 5 6 1 3 6 3 4 1 0 1 1 1 1 , max min         x x a a a a . Therefore we have proved that 12 5  z is sufficient for the non- existence of a partially informative equilibrium. When 2 1 12 5   z , we can’t use the argument above to rule out this equilibrium. So we conduct a grid search to determine whether there exists a medium which can benefit from reporting from another interval. We first numerically solve each medium’s profit if they stay in 137 the same interval, then compute the maximum profit each medium can obtain if it deviates to any other interval. Numerical results show that, as long as 0  M , there always exist one medium that can benefit from deviating to other intervals and jam the other, which confirms our previous result. Q.E.D. Proof of Proposition 5 Assume there exists an equilibrium that only one media is partially informative. We show that the uninformative medium always has incentive to deviate by jamming the rival through symmetrically imitating the rival’s stance. Note first that if this equilibrium satisfies the favorable criterion, then there exists at least one favorable out-of-equilibrium belief that reduces the media’s payoff if a medium deviates. From now on we restrict our attention to equilibria such that both media stances are optimal given these beliefs. We first analytically show when 0  M or ) 6 4 ( 4 z d M   the uninformative medium has incentive to jam the other. For the range of M that we can’t analytically compare, numerical analysis has been conducted to confirm the result. Without loss of generality, we assume media A is partially informative while media B is uninformative. In equilibrium 2 1  A n and 2 1  B n . Hence 0   . Similar to Proposition 4, the optimal profit equations are given by: ) 2 1 )( ( 18 ] ) 6 2 )( ( [ 2 z s s d M z s s s s d A B B A A B A           , and ) 2 1 )( ( 18 ] ) 6 4 )( ( [ 2 z s s d M s s z s s d A B B A A B B           . First, we can see that, in equilibrium we need ] , [ 1 i i A i a a s   and ] 1 , 0 [  B i s satisfies that ) , , ( max arg 1 i i A A s A i a a s s A    and ) ( max arg s s B s B i B   . We start with the case when 2  x . Although it is impossible to find closed form solutions of media stances for partially informative equilibrium, we can still show analytically 138 how the media optimally response when 0  M . Later we discuss the case for larger M. When M is zero, consumers don’t value facts at all. Solve the profit maximum for both media we have } 0 ), 2 1 ( max{ 4 3 2 1 z s A    and } 1 ), 2 1 ( min{ 4 3 2 1 z s B    . When 0  M and media A is partially informative, we know 2 1  A n , and 2 1  B n so that 0   . Because there is no closed form solution for the optimal stances, we cannot directly compare the profit of Media B under jamming or non-jamming. Instead we focus the relative profit change for media B when M changes from 0 to 0  dM in both cases. We start from the non-jamming case when B A s s  , which occurs if ] , 0 [ 2 1  t . We denote the optimal stance choices when 0  M and media B stays uninformative are A s 1 ˆ and B s 1 ˆ . The analysis when ] 1 , [ 2 1  t is similar therefore is omitted. We calculate media B’s profit changes in two cases: the profit change when media B jams media A by choosing A B s s 1 ˆ 1   so that consumers don’t know which one is partially informative; and the profit change when media B stays uninformative and chooses the optimal media stance B B s s 1 ˆ  . We first know 0 ˆ 0 1   M A dM s d , and 0 ˆ 0 1   M B dM s d . 21 Hence, when M increases from 0 to 0  dM , if B stays uninformative, then media A’s media stance increases from A s to A s 1 ˆ , and B B s s 1 ˆ  . If media B jams A with A B s s 1 ˆ 1 ~   so that two media stances are symmetric and consumers don’t’ know which media is really informative. It’s profit is: ) 2 1 ( 18 ) 6 3 )( ˆ 2 1 ( 2 1 2 z d z s d A B jam      . 21 Detailed analyses are omitted for brevity and available upon request. 139 Let’s denote A A A s s ds   1 ˆ . Then the profit change of Media B from B s to A B s s 1 ˆ 1 ~   by jamming the signal is ) 2 1 ( 18 ) ( ) 6 3 ( 2 ) , ( ) ˆ 1 , ˆ ( 2 2 1 1 z d ds z d s s s s d A B A B A A B jam B jam           If media B doesn’t jam A, it’s optimal choice is B B s s 1 ˆ  . To calculate the profit change due to the change of M, we take the total differentiation of M on B  : dM ds s dM ds s M dM d A A B B B B B B              ; When 0  M , )] 6 3 ( 2 [ ) 2 1 ( 18 1 | 0 z d z d M M B          ; ] ) 6 3 ( 2 [ ) 2 1 ( 18 1 | 2 2 0 z d z d s M A B nojam         . Therefore, dM d z d z d dM d B jam B         )] 6 3 ( 2 [ ) 2 1 ( 18 1 ; Or: B jam B nojam d dM z d z d d         )] 6 3 ( 2 [ ) 2 1 ( 18 1 ; Hence 0   B jam B nojam d d   , which means when M changes from 0 to dM, ) ˆ , ˆ ( ) ˆ 1 , ˆ ( 1 1 1 1 B A B A A B jam s s s s     . So media B has strict incentive to use media stance A B s s 1 ˆ 1 ~   to jam the report instead of using B s ˆ , which proves that the equilibrium of partially informative with one media doesn’t exist with x=2 when M is small. This result shows once M>0, media B suffers by staying as the only uninformative media because B A n n  . In fact, the reduction of B’s profit is so big that media B purposely chooses to jam A, to balance the expected number of facts between them. Now if there exists a partially informative equilibrium with 2  x , we can see there must exist an interval ] , [ 1 i i a a  such that ] , [ 1 i i A a a s   . It is easy to verify that the net difference of number of facts between media A and B is getting higher in this case. The loss of media B by staying as the only uninformative media 140 is even bigger. So media B will have stronger incentive to jam A when ] , [ 1 i i a a t   . This shows that when M is close to zero, it is never possible to find an equilibrium with only one partially informative media. Next we show the partially informative equilibrium disappears as M increases. The intuition is similar: as M increases, it might be too costly for media B to stay uninformative. We know for media B to earn positive profit, it must be the case that 0 ] ) 6 4 )( ( [ 3 1         M s s z s s d p B A A B B , we need       ) 6 4 )( ( B A A B s s z s s d M in order to guarantee the positive profit of media B. Then, if ) 6 4 ( 4 z d M   , then B p is negative regardless other variables. This essentially means that the disadvantage of staying uninformative report is so big that media B can’t obtain positive profit when consumers believe another media is partially informative. Under this case, media B will always deviate from B s ˆ to use signal jamming strategy and the partially informative with one media doesn’t exist either. Last, for the range of )] 6 4 ( 4 , 0 ( z d M   , profit comparisons between jamming and no- jamming can’t be signed analytically. We conducted a grid search to determine whether the uninformative medium has incentive to jam. We numerically solve the optimal A s 1 ˆ and B s 1 ˆ for given M, then compare the jamming and no-jamming profit of medium B. The numerical analysis confirms the previous result. We showed, as M increases, the uninformative medium’s profit is lower by staying as the only uninformative media comparing with jamming. Therefore, the uninformative medium will jam when )] 6 4 ( 4 , 0 ( z d M   . Q.E.D. 141 Proof of Proposition 6 From Proposition 4 and 5 we know consumers wouldn’t expect an equilibrium that both or one media provide informative updates about the state of the world. The only possibility is both media are uninformative so that consumers have no information updating. Under this case, 2 1   B A n n , therefore 0   . Similar to the result in Proposition 5 we have: } 0 ), 2 1 ( max{ 4 3 2 1 z s A    and } 1 ), 2 1 ( min{ 4 3 2 1 z s B    . We can see this equilibrium satisfies the favorable criterion since if the expected number of facts doesn’t increase when one media deviates, the media’s profit strictly decreases. Therefore there must exist some out-of-equilibrium beliefs that the expected number of facts is higher under the belief, but the media’s profit is lower. Q.E.D. Proof of Proposition 7 When 1 0 M M   , the monopoly generate uninformative report, and the duopoly media generate the uninformative report too. Hence competition doesn’t increase the informativeness of media reporting when M is small. However, when 3 M M  , the monopoly’s report is partially informative with at least two intervals, while duopoly media generate uninformative report. Therefore competition decreases the informativeness when M is large. Q.E.D. Proof of Proposition 8 When 1 0 M M   , the expected number of facts provide by the monopoly is 2 1 . While 3 M M  , the expected number of facts by the monopoly is 1 2 1   n . Under competition, both media are uninformative so 2 1   B A n n . Hence each medium provides fewer facts when 3 M M  . Q.E.D. 142 Proof of Proposition 9 Under duopoly if 2 1  z , then 2 1  A s and 2 1  B s and 0  Duo MP . The monopoly’s report is influenced by M. When 3 M M  , there exists partially informative with at least two intervals. Also notice as M increases, the media stance by monopoly moves further away from 2 1 and 0  Mon MP . Therefore when z and M are large enough the monopoly’s stance is more polarized than duopoly. But as 0  z , 0  A s and 1  B s in duopoly so that 2 / 1  Duo MP . While under monopoly, the media stances of all intervals are moving toward 2 1 when M decreases, so that 2 / 1  Mon MP . Therefore, when z and M is small, monopoly is less polarized than duopoly. Q.E.D. Proof of Proposition 10 Under uninformative reporting 2 1  s , so 12 1 1 0 2 2 1 U ) ( MB     dt t . Under partially informative with 2 intervals, 2 1 1  a and dt s t dt s t 2 ) ( 2 ) ( MB 1 2 2 0 2 1 I 2 1 2 1       . It is readily seen that when ) 1 ( 8 z d M   , 0 1  s and 1 2  s , therefore U 6 1 I MB MB   . Q.E.D. Proof of Proposition 11 When ) 1 ( 8 z d M   , from Prop 10 we know the media bias of Monopoly 6 1 1 2 0 2 2 ) 1 ( 2 ) 0 ( 2 1 2 1        dt t dt t MB Mon . The duopolies, however, provide uninformative report with } 0 ), 2 1 ( max{ 4 3 2 1 z s A    and . We can see when , then and , hence the average media bias . Therefore when z } 1 ), 2 1 ( min{ 4 3 2 1 z s B    2 1  z 2 1  A s 2 1  B s 12 1 1 0 2 2 1 ) (     dt t MB Duo 143 and M are large enough, at least the partially informative equilibria under monopoly with have higher media bias than duopoly. When z decreases, the media bias in duopoly increases. For example, when , then and . Hence on average. When , the monopoly provides uninformative report regardless of z. . Therefore we showed when z and M is small enough, monopoly has lower media bias than duopoly. Q.E.D. 2  x 6 1  z 0  A s 1  B s 3 1 1 0 2 ) 0 (     dt t MB Duo 1 M M  12 1 1 0 2 2 1 ) (     dt t MB Mon

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Creator Zhu, Yi (author)

Core Title Essays on commercial media and advertising

School Marshall School of Business

Degree Doctor of Philosophy

Degree Program Business Administration

Publication Date 04/17/2013

Defense Date 03/14/2013

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag advertising,commercial media,game theory,OAI-PMH Harvest

Format application/pdf (imt)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Dukes, Anthony (committee chair), Wilbur, Kenneth C. (committee chair), Dutta, Shantanu (committee member), Luo, Lan (committee member), Selove, Matthew (committee member), Tan, Guofu (committee member)

Creator Email yizhusc@gmail.com,zhuy@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c3-238277

Unique identifier UC11293625

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Legacy Identifier etd-ZhuYi-1562.pdf

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Document Type Dissertation

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Rights Zhu, Yi

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

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