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University of Southern California Dissertations and Theses
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Essays on digital platforms
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Essays on digital platforms
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Essays on Digital Platforms by Ilya Lukibanov 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 OR PHILOSOPHY (BUSINESS ADMINISTRATION) August 2022 Copyright 2022 Ilya Lukibanov Acknowledgements I am grateful to my advisor, Dina Mayzlin, for her major role in transforming me from an economist to a marketer, for her support and encouragement during ideas search and their development, and last but not least for her patience during my endless complains about USCbureaucracies. IamthankfultoOdilonCˆ amarawhohelpedtosharpenmydissertation models. Iwouldliketothankmyothercommitteemembersforprovidinginvaluablefeedback and giving insightful comments – Anthony Dukes, Lan Luo, Jo˜ ao Ramos, Fanny Camara. I also would like to thank S. Siddarth, Gerard J. Tellis, Kristin Diehl, Joseph Nunes, and Davide Proserpio for their support during the program. I am thankful to administrative staff who helped to make my journey smoother – Elizabeth Mathew, Doris Meunier, Jennifer Lim, and Julie Phaneuf. I am grateful to my peers who brightened up my time in the program – Aleksandr Zotov, Poet Larsen, Ivan Belov, Isamar Troncoso, Elisa Solinas, Yanyan Li, Mengxia Zhang, Amy Pei. I am indebted to my wife, Irina Osipova, without whom I would not be able to complete my dissertation and who always supported me during my PhD journey. I also indebted to my mother who sacrificed a lot to provide me with the best available education and raised me a decent human being. ii Table of Contents Acknowledgements ii List of Tables v List of Figures vi Abstract vii 1 Investments in content creation: A star effect 1 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.3 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.4 Comparison of equilibrium investment and effort under different competitive regimes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1.5 Equilibrium shares, number of viewers and payoffs . . . . . . . . . . . . . . . 19 1.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 2 Consumer Inferences under Targeting: Implication for Pricing 23 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2.2 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 2.3 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 2.3.1 Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 2.3.2 Customer problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 2.3.3 Firm problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 2.4 Strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 2.4.1 No technology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 2.4.2 Technology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 2.5 Equilibria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 2.5.1 Information improving marketing message . . . . . . . . . . . . . . . 37 2.5.2 Costly information reduction marketing message . . . . . . . . . . . . 41 2.5.3 Costless information reduction marketing message . . . . . . . . . . . 42 2.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 Bibliography 45 iii Appendix 49 Appendix to Chapter 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 Appendix to Chapter 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 iv List of Tables 2.1 Firm’s payoffs and customer’s beliefs. . . . . . . . . . . . . . . . . . . . . . . 37 v List of Figures 1.1 Timeline of the game . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.2 Equilibrium Effort and Investment as functions of initial number of viewers underdifferentregimes. PanelAshowsthemonopolycase; panelBshowsthe competitivecase. PanelsCfeaturesthestareffectcasewhentheeffortreaches the maximum amount first (all three previous cases for k = 0.3; c = 0.1; ρ = 0.3; ¯e = 1). Panel D features the star effect case when the investment reaches the maximum amount first ( k = 0.5; c = 0.1; ρ = 0.5; ¯e = 1). . . . . . . . . 15 1.3 Equilibrium Investment and Effort as a function of initial number of viewers under different regimes. Parameters: k = 0.3; c = 0.3; ρ = 0.3; ¯e = 1. . . . . 17 1.4 Equilibrium Platform’s share as a function of initial number of viewers under different regimes. Parameters: k = 0.3; c = 0.1; ρ = 0.3; ¯e = 1. . . . . . . . 20 1.5 EquilibriumUtilityandProfitasafunctionofinitialnumberofviewersunder different regimes. Parameters: k = 0.3; c = 0.1; ρ = 0.3; ¯e = 1. . . . . . . . 21 1.6 EquilibriumUtilityandProfitasafunctionofinitialnumberofviewersunder different regimes. Parameters: k = 0.3; c = 0.5; ρ = 0.3; ¯e = 1. . . . . . . . 22 2.1 Equilibria when c τ = 0.04, c a = 0.01. . . . . . . . . . . . . . . . . . . . . . . 39 2.2 Equilibria when c τ = 0.02, c a = 0.08. . . . . . . . . . . . . . . . . . . . . . . 40 2.3 Equilibria when c τ = 0.05, c a = 0. . . . . . . . . . . . . . . . . . . . . . . . . 43 A.1 Best response functions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 A.2 Intersection of the best response functions. . . . . . . . . . . . . . . . . . . . 52 A.3 Existence of the targeting equilibrium for different costs. . . . . . . . . . . . 62 vi Abstract Thisdissertationincludestwochapterswithafocusondigitalplatformstopics. Theobjective of the first chapter is to understand the phenomenon of the investment into content creators by the platforms in the context of digital platforms. I consider platforms like YouTube, Twitch, and TikTok where some users earn money by creating content consumed by other users. Theseplatformscanrecommendcontentcreatorsinsidetheplatformonvariouspages. These recommendations help content creators to grow their audiences and effectively serve as investments into them. The content creators generate some revenue on the platform (e.g., paid subscriptions, advertisements). The platform and the content creator then split this revenue. This chapter tries to understand how competition between the platforms for content creators affect the equilibrium investment into content creators, revenue split and profits. I find that the platform has incentives to invest less into content creators compared to the monopoly case when there is some competition between the platforms. Moreover, the platform does not invest into big streamers if there is a star effect in the market. The welfare implications mainly depend on the model parameters. There only two relationships that always hold: the platform prefers the monopoly over the competition and the content creator prefers competitive regime over the monopoly. However, the star effect might the most preferred (the second best) or the least preferred option for the content creators (platform) depending on the parameters. The second chapters studies how targeting affects consumer’s willingness to pay and equilibrium pricing decisions. I consider a situation where a firm uses internet advertising to make customers aware about its product. The customer seeks for a product that is good vii fit for him. The firm has initial message about its product based on truthful claims about the product. However, the claims cannot convey all the information that the customer needs to understand whether the product is a good fit for him. Therefore, the message is characterized by its precision – how likely the customer infers that the real good fit product is good fit for him. The firm can purchase a targeting technology that helps to analyze the customer’s preferences to create a new signal. The new signal might have higher or lower precision than the original signal. There are four equilibria emerge. If the precision of the originalisnottoohigh,thefirmdoesnotpurchasethetargetingtechnology,servesthewhole market and sets a relatively low price. If the precision of the original is sufficiently high, the firm does not purchase the targeting technology, serves the customers who think that the product is a good match for them and sets a relatively high price. If the new signal has higher precision and the cost to increase in precision ration is relatively low, the firm purchases the targeting technology, serves the customers who think that the product is a good match for them and sets a relatively high price. Finally, when the new signal is vaguer than the original one and the costs of the new message are really low, the firm purchases the targeting technology, serves the whole market and sets a relatively low price. I find that the price might be non-monotonic in the precision of the initial message. viii Chapter 1 Investments in content creation: A star effect 1.1 Introduction In the last two decades, the rise of social media platforms has enabled and expanded the abilityofcontentcreatorstoconnectwithanaudience. PlatformssuchasTikTok,YouTube, Instagram, and Twitch have transformed popular entertainment. The platform’s basic deci- sion,andonethattheplatformiscontinuouslymakingforeachuser,iswhichcontentcreator to recommend at any point in time. We can think of the recommendation as an investment by the platform into the content creator since recommendations drive the growth of the cre- ator’s audience and also imply an opportunity cost to the platform. According to the Black Girl Gamers group, Twitch plays a large role in the content creator’s success, ”Viewer count isn’t just achieved in a vacuum, it is affected by endorsements, ranking, exposure, opportu- nities from brands including the streaming platform itself, algorithmic visibility—there are many variables that affect viewer count over time 1 .” The platforms play an important role in this communication – they navigate users in the abundanceofdifferentcontentcreators. Fromthecontentcreators’perspective,theplatform recommendations are investment into their growth. The platform could invest in content creators in other ways. For example, Facebook was widely criticized for granting special 1 https://www.pcgamer.com/twitch-streamer-income-leak/ 1 privileges to millions of “V.I.P” users, including exempting them from moderator controls 2 . TwitchsourcecodeleakshowedthatTwitchwhitelistssomeofthepopularcontentcreators, so they cannot be banned 3 . This phenomenon is not limited to the new generation of the creative professions. Ac- tors, athletes, writers, lawyers, and professors also face the same circumstances – their agent/employer can choose a level of investment into their successful careers. For example, anassistantprofessorcanreceiveanincreasesresearchbudget,oruniversitycanpromoteher work in media. However, the university balances two goals: to raise a successful academic and to retain this scholar in the university. If the university invests too much, the faculty becomes successful and other universities would try to poach them. Therefore, the second goal creates incentives to invest less than it would be optimal if the faculty commits to stay at the university. The platforms face a similar issue: they want their content creators to have more fol- lowers and viewers, but it makes them more attractive to other platforms. The platforms invest into content creators by allocating space on the main page (and other popular pages). For example, Tyler Blevins, mostly known as Ninja, increased his average viewership from about 4.5k in March 2017 to more than 100k in March 2018 on Twitch 4 . The platform played an important role in this growth – at this point, Twitch’s recommendation system promoted streamers with the highest number of viewers on the main page. However, these investments might be counter-productive. In summer of 2019, Mixer, a rival streaming plat- form, poached Ninja with a multi-million contract that is speculated to pay up to $30M over a few years 5 . This and a few others acquisitions helped Mixer to increase its share in the streaming platform market 6 . 2 https://www.wsj.com/articles/facebook-files-xcheck-zuckerberg-elite-rules-11631541353 3 https://cyberpost.co/twitch/whitelisted-streamers-found-among-leaked-twitch-files/ 4 https://twitchtracker.com/ninja/statistics 5 https://www.pcgamer.com/ninja-allegedly-made-dollar20-30-million-by-moving-to-mixer/ 6 https://www.fool.com/investing/2020/03/19/amazons-twitch-is-still-losing-ground-to-microsoft.aspx https://www.digitaltveurope.com/2019/12/23/twitch-still-top-for-game-streaming-but-mixer-starts-to- make-a-dent/ 2 This raises a question whether platforms should focus on investing in small or big streamer. Twitch small content creators complained that it is hard to grow on the plat- form because it does not promote them 7 . Twitch did not react act to this critique for years. Interestingly, around the time when Mixer poached a few of the Twitch’s top streamers, Twitch introduced “Small communities that you might like” section on the main page and started to include small channels in “Live channels we think you’ll like” section at the top of the main page. This example shows that the competition for the content creators might affect the platforms’ investment priorities (e.g., invest into small or big streamers). What is the optimal investment level incurred by the platform to promote the content creator? Higher investment level increases the content creator’s number of viewers that translates into higher potential revenues. However, the viewership increase makes the con- tentcreatormoreattractivetootherplatforms. This, inturn, improvesthecontentcreator’s negotiation power and it might lead to a lower profit. The other platforms might have dif- ferent preferences for the streamers (i.e., competitive regimes) that can vary over time. For example, Mixer decided to poach big Twitch streamers in summer of 2019. This leads to the effect that we call “star effect”, meaning that the other platform prefers one streamer with 100k viewers over 100 streamers with 1k viewers. We ask the following research questions. First, how should platforms optimally invest into building stars? Second, how does compe- tition in the market for content creators affect those investment decisions? Finally, what is the impact of the star effect on platform’s and streamers’ profits? We propose a model with two players: an investor and a talent. The talent a way to create value for the investor, e.g. the content creator have some audience that generates revenues that are split between the players, or the professor produces researches that help to improve university position in rankings that, in turn, attract talented students. The value generation process can be enhanced in two ways: 1) the investor can invest some amount into the talent, e.g., the platform can allocate some amount of promotional space to the 7 https://www.youtube.com/watch?v=fYjTKluzSss 3 content creator, or the university can, for example, reduce teaching load or provide more media attention; 2) the talent can exert a costly effort to improve their skills or output, e.g. the content creator can spend more to improve the content quality or the faculty can spend more time on the research. We assume that the effort and the investment level are common knowledge, but they are not verifiable (i.e. they cannot contract on the effort and theinvestmentlevel). Theseactionsincreasetheviewershipinthenextperiod, inwhich, the talent receives an outside offer. The talent takes this offers and (re)negotiates the revenue split with the investor. We show that if the investor is a monopoly in the market, it increases the investment amount with the current value generation size. Moreover, if there is a competition in the marketfortalents,buttherearenoincreasingreturnsfortheinvestorinthevaluegeneration size, the investor still increases investment size with the value generation size. Finally, we show a counter-intuitive result. If there is the star effect in the market for talents, i.e. increasing returns to the value generation, the investment amount becomes non-monotonic inthecurrentvaluegenerated–theinvestmentamountinitiallyincreasesandthendecreases. Ourintuitiontellsusthattheinvestorwouldwanttoretainthelargesttalentsbyinvestingin them a lot. However, our model suggests that the investor would not invest into big talents under the star effect because it will increase their negotiation power and it will decrease the investor’s profit. The structure of our paper is the following. In Section 1.2, we discuss the related liter- ature. In Section 1.3, we propose our model. In Section 1.4, we discuss the investment and the effort choices. In Section 1.5, we discuss the welfare implication of switching between competitive regime. We conclude and discuss limitation and direction for future research in Section 1.6. 4 1.2 Literature Review Our paper contributes to three literature threads: 1) labor economics literature on firm investment into employees, 2) the star effect literature, which includes the papers on the superstar effect in the film industry and the work on the star effect in the corporate finance literature, and 3) the literature on the talent and creative professions. Weexamineanenvironmentwhereaninvestorcaninvestintoimprovingvaluegeneration potential of a talent. We find that the investor has incentives to under-invest. This is not a novel result in the labor economics literature on firm’s investments into its employees. But we demonstrate this effect in a novel context – we show that this effect is driven by the natureofthecompetitioninthemarketfortalents. Inalaborliterature,theemployerinvests into improving the worker’s skills. This literature shows that the employer has incentives to under-invest into the worker’s general skill set. Thishasbeenshownindifferentcontexts. Grout(1984)analyzesthenegotiationbetween a union and a firm under the absence of binding contracts. He finds that if the union has any negotiation power, the firm under-invests. Our model uses the same framework (Nash bargainingsolution)andproducesparallelresults,butitalsoenrichestheresult. Theinvestor still has incentives to under-invest, but the shape of the investment function of the value generationpotentialdrasticallychangesunderdifferentcompetitiveregimes. Manning(1987) proposes a unified framework for union bargaining model which reflects the main results of Grout (1984). Crawford (1988) finds that if firms can use only short-term contracts, the parties under- investinlong-termrelationshipbecauseitreducesownnegotiationpowerinthenextcontract negotiation cycle. Acemoglu (1997) finds that in a frictional labor market, the future em- ployer enjoys the workers’ productivity gains that creates incentives to under-invest into general skills. We use a similar logic in our model – the competitive investor can poach the talent from the current investor and enjoy talents’ current audiences obtained through the past investments. Acemoglu and Pischke (1999) show that firms invest into general human 5 capital, but it transforms part of this capital into the firm-specific. Interestingly, Holden (1999) finds that risk aversion can reduce the amount of under-investment. In the labor market context, the workers with high seniority (i.e. relative tenure) get compensated more than their junior peers (Hashimoto, 1981; Carmichael, 1983). In our context, it translates into talents with high revenue generation potential (i.e., that stayed with the investor for longer period of time) will have a higher revenue split share. Wecontributetothislaborliteraturebyconsideringhowthecompetitivestructureinthe market for workers, or in our case “talent,” alters the firm’s well-known under-investment decision. In our paper, we examine how the firm’s investment strategy is affected by the star effect. Here, we define the star effect as a competition regime in the market for talents under which the investors have increased returns to the value generation potential of the talent. The star effect has been previously studied in the context of film (Elberse, 2007), theater (Han and Ravid, 2020), corporate finance (Malmendier and Tate, 2009), and digital goods (Brynjolfsson et al., 2010). In a seminal paper, Rosen (1981) introduces the formal modellingapproachtothesuperstareffectliteraturebyshowingthatgivenasetofreasonable assumptions, we can model a market equilibrium with the superstar effect. We take the existence of the star effect as an assumption and examine the effect of it on the investment decision. Brynjolfssonetal.(2010)proposesdriversforthesuperstareffectindigitalmarkets. Our main example for the model, content producers, is a “digital service” in its nature. We examine the implication of the star effect in this market. In a movie context, Elberse (2007) finds that an addition of a star to a movie increases the movie revenues, but it does not affect the movie studio market valuation. In a theater context, Han and Ravid (2020) estimate the value of the theater stars and finds that the stars capture most of their value. These two papers show that star talents generate profits, but they are not able to capture it. In a CEO context, Malmendier and Tate (2009) find that CEOs that win prestigious business awards under-perform compared to their peers, but 6 enjoy higher compensations. It shows that it is not always profitable to keep stars. We also find that the investor might not want to invest into stars, but the mechanism is completely different. In our context, the investor would not invest into big talent under the star effect because it would increase their negotiation power too much. We contribute to the star effect literature by adding the investment decision. Finally, we model investments into workers whose main occupation are creative profes- sions and call them talents. Caves (2003) provides an exhausting overview of the compen- sation structures in “old” creative professions: artists, authors, musicians. We assume that the talent and the investor share the profit, but it might not be true in all scenarios. In these cases, the salary can still be interpreted as a share of profits generated by the talent. Chisholm(1997)examineswhatdrivesthemoviestudios’decisiontoofferprofitsharingver- sus the fixed payment. In the sports literature, Vohra (2020) shows that athletes collectively enhance their welfare by introducing caps on their salaries. Another important emerging literature studies online talents/ content creator. Jain and Qian (2021) propose a model to examine the optimal platform compensation behavior. In particular, they examine how growth of the platform affects and growth of the audience size affects the equilibrium profit sharing. This is close to our question, but we mainly focus on the investment decisions by the platform rather than on the compensations themselves. Lu et al. (0) empirically study how the audience size affects the donation behavior on live streaming platforms. 1.3 Model We consider a model of strategic interaction between a platform (she) and a content creator (he). We assume that both the platform and the content creator can take costly actions (investmentoreffort,respectively)toincreasethecontentcreator’saudiencesize. Thelarger audiencegeneratesmoreover-allrevenuethatissubsequentlysplitbetweentheparties. This creates a trade-off for the platform: her investment increases the content creator’s audience, 7 which in turn helps generate more over-all revenue. However, the platform’s investment increasesthenegotiationpowerofthecontentcreatorthroughtheoutsideofferfromanother platform. We study how these effects impact the investment and the effort decisions when we vary competition regimes in the markets for content creators. Content creator. The content creator has v 1 (> 0) viewers on the platform at period 1. The content creator receives share (1− α 1 ) of period 1 revenue, π 1 (v 1 ). We assume that the share α 1 ∈ (0,1) was negotiated before the start of the game. We also assume that the numberofviewersstaysconstantovertimeintheabsenceofanyfurtherinvestmentfromthe platform or effort from the content creator. We defined the number of viewers in the second period as v 2 (i,e). We assume that the number of viewers in the second period increases if the platform invests some amount, i(≥ 0) (we will discuss in more detail the platform’s investment below), and/or the content creator exerts effort, e(≥ 0). We further assume that the effort cannot exceed a certain amount, 8 ¯e, and the cost of effort is ρe 2 , where ρ > 0. We also assume that the content creator’s effort choice is not directly observable by the platform and is non-contractible. 9 However, the platform infers the content creator’s effort in equilibrium. We assume a multiplicative effect of content creator effort and platform investment on the number of viewers in the second period, but separable with respect to each other. 10 That is, at the beginning of the second period, the content creator’s number of viewers is the following: v 2 (i,e)≡ (1+i+e)v 1 . After v 2 (i,e) is observed, the content creator receives an outside offer o(v 2 (i,e)). Given the outside offer, the content creator and the platform renegotiate their revenue split. We assume that they use the Nash bargaining solution to divide period 2 revenue, π 2 (v 2 (i,e)). The effort and the investment level affect the negotiated share; therefore, the equilibrium content creator’s share, (1− α 2 (i,e)), dependents on them. At the end of the second period, 8 This assumption follows from the fact the content creator cannot stream or improve his skills more than 24 hours a day. 9 Inreality,theplatformcannoteasilyobserveacontentcreatorimprovinghisstreamingskillsandquantify it to write a related contract. 10 Assuming a multiplicative effect might be more reasonable in this context, but it becomes computation- ally intractable. 8 the revenue π 2 is realized, and the content creator receives (1− α 2 (i,e))π 2 (v 2 (i,e)). We assumethatthereisnodiscountingbetweentheperiods. Thecombinedutilityofthecontent creator from both periods has the following form: U(i,e) = (1− α 1 )π 1 (v 1 )− ρe 2 +(1− α 2 (i,e))π 2 (v 2 (i,e)) (1.1) Platform. The platform observes the initial number of content creator’s viewers. She choosestheinvestmentamount,i,attheendofthefirstperiodandincursthecost C(i)≡ ci 2 , wherec∈ (0,1). Thisinvestmentneednotnecessarilybemonetaryinthiscontext. Thecost ofinvestment,C(i),couldbetheopportunitycostofnotfeaturingothercontent(whetherads or links to other content creators) on her main page. For example, consider the platform’s choice to feature the content creator on her main page. Here, the cost of featuring the content creator is the opportunity cost of not featuring the other content creators, where c could be related to the number of competitive content creators on the platform, and i is the frequency with which the platform features the focal content creator. The investment incurred by the firm is not observable by the content creator and is non-verifiable. 11 We impose the restriction that the investment level cannot be negative in our context. The platform receives α 2 (i,e)π 2 (v(i,e)) share of the second period revenue at the end of the game. The platform has the following profit function: Π( i,e) =α 1 π 1 (v 1 )− ci 2 +α 2 (i,e)π 2 (v 2 (i,e)) (1.2) Outside offer. The outside offer represents the competitive structure in the market for the content creators. We assume the following flexible functional form of the offer: o(v 2 (i,e)) =k((1− λ )v 2 (i,e)+λv 2 (i,e) 2 ), 11 The platform can customize the content shown to different viewers; therefore, the overall investment level i is not easily observable. 9 Period 1 Period 2 Initial share, α 1 Initial viewers, v 1 Payoff realization, π 1 (v 1 ) Platform invests i Streamer exerts effort e Viewers realization, v 2 (i,e) Outside offer arrives Platform share, α 2 (i,e) Contract renegotiation Payoff realization, π 2 (v 2 (i,e)) Figure 1.1: Timeline of the game where λ ∈ [0,1] and k ∈ [0,1). The k parameter represents the fit between the content creator and the other platform. The outside offer function has two main components: linear and quadratic, where λ parameter represents the relative importance of these components. When λ = 0, the outside offer is linear in the number of viewers, meaning that the other platform values each viewer equally. We call this the competitive case because it is the simplest form for the outside offer function. When λ = 1, the outside offer is quadratic in number of viewers meaning that the other platform values having one content creator with 10,000 viewers more than having ten content creators with 1,000 viewers each. We call this the star effect case because the other platform values content creators with a high number of viewers disproportionately more than small content creators. Finally, when k = 0, the outside offer is zero, and the platform is a monopoly in the market for content creators. Renegotiationproblem. WeassumethattheplayersusetheNashbargainingsolution to determine the division of the revenue after the arrival of the outside offer. Therefore, the renegotiation problem has the following form: max α 2 α 2 π 2 (v 2 (i,e))((1− α 2 )π 2 (v 2 (i,e))− o(v 2 (i,e))) (1.3) where α 2 is the share that the platform receives. The timing of the game is provided in Figure 1.1. 10 Equilibrium We are looking for the subgame perfect Nash equilibrium (SPE) of this game where the platformandthecontentcreatorchoosetheinvestmentlevelandtheeffort, respectively. We solve the game by backward induction. We start with the renegotiation problem. Then, we analyze the best response functions to find the equilibrium. Negotiation. Weassumethattheper-periodrevenuegeneratedfromstreamingisequal to the number of viewers: π (v t )≡ v t . This could be the case (as it does in our context) if the subscribers pay a fixed amount each month. Substituting the profit into Equation 1.3 and differentiating, we obtain the platform share following the renegotiation: α ∗ 2 = 1 2 − o(v 2 (i,e)) 2v 2 (i,e) . (1.4) This equation shows that the platform’s share decreases in the size of the outside offer. However, the equilibrium share behavior as a function of the initial number of viewers is not obvious. We will study it in the following sections. We assume that the content creator leaves the platform when the outside offer is bigger than the profits that he receives from the platform, 12 i.e. (1− α 2 )π (v 2 (i,e))− o(v 2 (i,e))< 0. Substituting the expression for α ∗ 2 into the inequality, we obtain the following condition for leaving: π v 2 (i,e) <o v 2 (i,e) . This condition means that the content creator leaves when the other platform offers more than he generates on the current platform. Investmentstage. WesubstitutethesharefromEquation1.4intothecontentcreator’s utility(Equation1.1)andthefirm’sprofit(Equation1.2). Differentiatingthecontentcreator utility and the platform’s profit with respect to effort, e, and investment, i, respectively, we obtain the best response functions for the content creator’s effort and the platform’s investment. See Appendix for the effort best response function derivation. 12 Alternatively, we can assume that the content creator leaves with some exogenous probability. However, this does not qualitatively change the results. 11 e br (i;· ) = min v 1 (1+k(1− λ ))+2kλv 2 1 4ρ − 2kλv 2 1 + 2kλv 2 1 4ρ − 2kλv 2 1 max{0,i}, ¯e , if v 2 1 < 2ρ kλ ¯e, if v 2 1 ≥ 2ρ kλ (1.5) i br (e;· ) = max v 1 (1− k(1− λ ))− 2kλv 2 1 4c+2kλv 2 1 − 2kλv 2 1 4c+2kλv 2 1 min{e,¯e}, 0 (1.6) There are three main insights from these best response functions. First, when λ = 0 (competitive case) or k = 0 (monopoly case), the equilibrium investment end effort are independent–theeffortofthecontentcreatordoesnotdependontheplatform’sinvestment and vice versa. Second, for λ > 0, the effort weakly increases in the investment amount. Last, for λ > 0, the investment weakly decreases in the effort level. This means that any amount of the platform investment motivates the content creator to work harder. Moreover, the more the platform invests, the more the content creator exerts effort. On the contrary, the platform does not want the content creator to grow too much because he will gain too much negotiation power in the second period. The effort increases the audience in the second period; therefore, the platform tries to balance this effort out by investing less. The investment amount decreases in the effort level of the content creator. The effort best response function has 4 ρ − 2kλv 2 1 term in the denominators. It seems that this term should make the whole function to behave bad. 13 However, this best response function is actually well-behaved. For example, if we consider it as a function of v 1 : at the left of the supposed discontinuity, the expression equals to ¯e due to the restriction on the maximum level. At the right it always equals to ¯e due to the maximization problem. Therefore, the effort best response function is continuous at this point. In the following proposition, we abuse the notation to make it easier to follow the cases. In this paragraph, we explain the notation. The best response functions can intersect in 13 In particular, we face the following issue: lim 4ρ − 2kλv 2 1 →0 + e br (i;· )= ¯e (or it equals to infinity if we drop the condition on the upper bound) and lim 4ρ − 2kλv 2 1 →0 − e br (i;· )=−∞ . This means that the effort weakly increases in the beginning, but then drops to minus infinity. 12 three ways: 1) in the interior region of effort and investment; 2) on the bound of either function; or 3) at corner of both functions. We define the first case as the interior solution and denote the resulting effort and investment as e i andi i . These functions are basically the best response function without the min, max function boundaries. We formally define all functionsinAppendix. Inthesecondcase, wewillhaveapairoftheboundfunctionandthe bestresponsefunctiontakenatthisboundvalue. e b denotestheeffortbestresponsefunction evaluated at i = 0. i b denotes the investment best response function evaluated at e = ¯e. However, e i , i i , e b , i b can mean both the equilibrium points and the functions that depend on the model parameters. We introduce the following notation to distinguish between these cases: plain use of e i and i i means that we discuss the points and (e i (· ),i i (· )) means that we discuss them as functions of v 1 ,k,c,ρ,λ parameters. Now, we are ready to introduce the equilibrium of the game. Proposition 1. The game has a unique subgame perfect equilibrium that has the following form. 1. In the monopoly and the competitive cases, the platform invests i ∗ = i i (k,· ) and the content creator exerts effort e ∗ = min{e i (k,· ), ¯e}. 2. In the star effect case, there are four possible outcomes: a. Theplatforminvestsi ∗ =i i andthecontentcreatorexertseffort e ∗ =e i ife i (· )≤ ¯e and i i (· )≥ 0. b. i ∗ = 0 and e ∗ =e b if e b (· )< ¯e and i i (· )≤ 0. c. i ∗ =i b and e ∗ = ¯e if e i (· )≥ ¯e and i b (· )> 0. d. i ∗ = 0 and e ∗ = ¯e if e b (· )≥ ¯e and i b (· )≤ 0. 3. The content creator leaves if π (v 2 (i ∗ ,e ∗ )) < o(v 2 (i ∗ ,e ∗ )). If he stays, the platform receives α ∗ 2 = 1 2 − o(v(i ∗ ,e ∗ )) 2v(i ∗ ,e ∗ ) share of π (v 2 (i ∗ ,e ∗ )). 13 InAppendix, weshowthattheequilibriumofthisgameisunique. Then, wecharacterize the equilibrium in terms of the function that are described above. The first part of the proposition states the investment level and the effort level under the monopoly and the competitive regimes. The second part describes the equilibrium outcome under the star effect regime. It takes care of the boundary conditions that makes it look a bit complicated, but it is just a description of all possible interactions. There is an important implication of this proposition. Under some conditions, the platform invests nothing under the star effect regime because of two mutually exclusive, but related reasons – 1) any investment increases the content creator’s negotiation power too much; or 2) the content creator is too valuable foranotherplatform,andheleavesinthesecondperiodforsure. Weanalyzetheequilibrium effort and investment choices as functions of parameters in the following sections. 1.4 Comparison of equilibrium investment and effort under different competitive regimes In this section, we study the equilibrium investment and effort choices. We start with the monopoly case to establish a base scenario in which there is no competition for content creators. Then, we analyze the competitive case to isolate the effect of competition on the equilibrium effort and investment. Finally, we study the star effect case to understand how the intensity of competition for stars affects the effort and the investment. Monopoly. Let us substitute the monopoly parameter (k = 0) into e i (· ) and i i (· ) to understandtheirbehavior. Wereceivethefollowingoptimalinvestmentandeffortequations: i ∗ m = v 1 4c and e ∗ m = min{ v 1 4ρ , 1}. We plot the equilibrium effort and investment in panel A of Figure 1.2 as a function of initial number of viewers, v 1 . The main result in this case is that the platform investment increases in content creators’ initial viewership size. A monopoly platform invests more into bigger content creators because they have higher return on investment. The second insight is that the content creator’s effort choice is weakly 14 Figure1.2: EquilibriumEffortandInvestmentasfunctionsofinitialnumberofviewersunder different regimes. Panel A shows the monopoly case; panel B shows the competitive case. Panels C features the star effect case when the effort reaches the maximum amount first (all three previous cases for k = 0.3; c = 0.1; ρ = 0.3; ¯e = 1). Panel D features the star effect casewhentheinvestmentreachesthemaximumamountfirst( k = 0.5; c = 0.1; ρ = 0.5; ¯e = 1). 15 increasing in the audience size. This result is quite intuitive: the larger the audience side, themoremoneythecontentcreatormakesfromit, themoreeffortitmotivateshimtoexert. The linearity of the investment and the effort follows from two facts: the negotiated share is constant irrespective of the initial audience size and the revenue is assumed to be linear in the audience size. Competition. We substitute the competitive parameter (λ = 0) into e i (· ) and i i (· ) to obtain i ∗ c = v 1 (1− k) 4c and e ∗ c = min{ v 1 (1+k) 4ρ , 1}. We plot these equation in panel B of Figure 1.2 as functions of initial number of viewers, v 1 . We see that the firm’s investment still increases in content creators’ initial audience size. However, the platform invests less compared to the monopoly case for a given number of initial viewers. In this case, the platform still has higher return on investment for bigger content creators. However, the platform’s ROI shrinks because she has to give up a higher revenue share to the content creator compared to the monopoly case. Similarly to the monopoly case, the content creator effort weakly increases with the audience size. However, he puts more effort given the same audience size compared to the monopoly case because he is additionally motivated by the future outside offer. The equilibrium investment and effort are still linear because the equilibrium negotiated share is constant given the parameters and the revenue function is assumed to be linear. Star effect. Substituting the star effect parameter ( λ = 1) into i i (· ) and simplifying it, we find the interior star investment level: i ∗ s = (ρ − 2kρv 1 − kv 2 1 )v 1 4ρc +2kv 2 1 (ρ − c) . We plot it with boundary extensions in Panels C and D of Figure 1.2. The star effect adds an interesting twist to the previous results – the investment level is not monotonous in the number of viewers. It initially increases and then declines. The intuition behind this result is that the investment makes the content creators more valuable to the other platform, and this results in a lower negotiation power for the platform in the subsequent period. Therefore, theplatformpreferstoinvestlessintocontentcreator’sgrowthtokeephernegotiationpower high. Moreover, theplatforminvestslessgiventhesamecontentcreator’saudiencesizethan 16 Figure 1.3: Equilibrium Investment and Effort as a function of initial number of viewers under different regimes. Parameters: k = 0.3; c = 0.3; ρ = 0.3; ¯e = 1. in the monopoly case – the same result as in the competitive case. We formalize this result in the following corollary. Corollary 1. Any competition leads to lower investment levels compared to the monopoly case. A competition leads to a lower negotiation power for the platform that in turn disrupts herincentivestoinvest. However,thenatureofcompetitionaffectshowmuchtheinvestment is disrupted for different audience sizes. We plot only equilibrium investments in Figure 1.3 panel A to compare them across regimes. We see that the star effect is beneficial for small content creators compared to the plain competition because it almost does not disrupt the platform’s incentive to invest. However, the large content creators are a way worse-off under thestareffectcomparedtothecompetition. Moreover, wewanttoknowhowtheinvestment levelchangeswhenthestareffectdegreeinthemarket, λ ,increases. Weshowhowthedegree of disruption varies with the degree of the star effect in the following corollary. Corollary2. Increaseinthedegreeofstareffect, λ , leadstoincreaseininvestmentsforcon- tent creators with small audiences, v 1 ∈ (0,¯v 1 ). However, it leads to decrease in investments for content creators with large audiences, v 1 > ¯v 1 . 17 This corollary suggests that the higher the degree of the star effect the more the small content creators are better off. However, it simultaneously exacerbates the underinvestment into the big content creators. Substituting the star effect parameter ( λ = 1) into e i (· ) and simplifying it, we find the interior star effort level: e ∗ s = (c+2ckv 1 +kv 2 1 )v 1 4ρc +2kv 2 1 (ρ − c) . The effort increases before it reaches the maximumamount. Itlookslessintriguingthanthechangeininvestment, buttheresultsare actually similar. The content creator exerts more effort given the same number of viewers than in the monopoly case and this fact echoes Corollary 1. Moreover, the change in the effort level when we move from the competitive case to the star effect case mirrors the investment dynamic. When we increase the degree of star effect, λ , small content creators exert less effort, but big content creators exert more effort. More interestingly, the threshold for this change is the same as for the investment. Let us summarize these observations more formally in the following proposition. Corollary 3. a. Any competition weakly increases effort. b. An increase in the degree of star effect, λ , decreases effort for content creators with small audiences, v 1 ∈ (0,¯v 1 ) and increases effort for content creators with big audiences v 1 > ¯v 1 . This corollary shows that the switch from the monopoly to some competition in the market for content creators motivates them to exert more effort. The content creator un- derstands that his effort will attract more people and it will increase his negotiation power through the outside offer. However, the effect varies for content creators with different audi- ence sizes. The small content creators gain less and less of the negotiation power in the next period as the degree of the star effect increases; therefore, they become less incentivized to exert effort. On the contrary, the big content creators gain a lot of negotiation power from the increase in the degree of the star effect; thus, they are incentivized to exert more effort. 18 The maximum amount of effort can be interpreted as choosing streaming as the main occupation. Giventhisformulation,themorecompetitioninthemarketforcontentcreators, the easier they can decide to devote all their time and efforts exclusively to succeed in this area. 1.5 Equilibrium shares, number of viewers and payoffs In this section, we discuss equilibrium profit shares and payoffs. We cannot change the competition structure; therefore, we would not go into detailed derivations and comparisons between regimes. Theplatform’sequilibriumshareisconstantinthemonopolyandthecompetitionregimes. This fact follows from the Nash bargaining solution and assumptions on the outside offer in these cases. It means that the content creator receives the same share of income irrespec- tive of his initial number of viewers. However, bigger content creators receive more money because they generate higher revenue than smaller content creators. As expected, content creatorsreceivehighershareunderthecompetitionthanunderthemonopoly. Thestareffect case changes this dynamic – the platform’s share decreases with the number of viewers. The platform share starts at the monopoly level, then it gradually decreases to the competition level as the content creator’s number of viewer increases, and then it steadily drops to zero. The small content creators are worse-off compared to the competitive case because they re- ceive a smaller share. Moreover, they exert lower efforts, but receive higher investment from the platform, so they have almost the same number of viewers in the following period, but they earn less because of the lower share. Now, let us look at what happens to the firm’s profit and to the content creator’s utility. Theresultshaveamorecomplexstructurethantheshareresult; therefore,itishardtomake any general statement about them. The result for the platform is relatively intuitive: she prefers the monopoly scenario compared to the other two because it provides a higher profit. 19 Figure 1.4: Equilibrium Platform’s share as a function of initial number of viewers under different regimes. Parameters: k = 0.3; c = 0.1; ρ = 0.3; ¯e = 1. There are two main reasons for that: the platform always gets half of the generated revenue and the platform invests more which leads to the overall bigger revenue. The platform generally prefers the competitive regime over the star effect in terms of the initial number of viewers. The only exception is a region for some range of small content creators. However, to make more general statements, we need to make an assumption on the distribution of the content creators’ initial viewership and compute the expect profit from all content creators. In reality, we observe a distribution that is similar to the exponential distribution; therefore, we might expect that are parameters under which the platform prefers star effect over the star effect. The results on the profits under different regimes is close to and partially due to the investment choice result. The higher platform’s equilibrium share lead to the higher profitunderthestareffectandthereforetheplatformprefersthestareffectforsmallcontent creators. The competition is more preferable for the firm for big content creators. There are a few reasons for this: the content creators have less negotiation power, which leads the firm to invest more which in turn increases the revenue. At the same time, the firm obtains a higher share of this bigger revenue. Contentcreator’spreferencesovertheregimesarelessstable. Thecontentcreatoralways prefers the competitive case over the monopoly case because he receives a higher revenue share and this fact over-weights lower investments by the firm. However, the preference for the star effect regime varies a lot. Small content creators prefer the star effect over the 20 Figure 1.5: Equilibrium Utility and Profit as a function of initial number of viewers under different regimes. Parameters: k = 0.3; c = 0.1; ρ = 0.3; ¯e = 1. monopoly. Intuitively, they have a higher negotiation power which leads to a higher share of the revenue. At the same time, the effort is marginally lower than in the monopoly and the investments are marginally higher – these two effects cancel out each other and the content creator receive more money because of the higher share. If the platform’s costs of investment are high enough, the star effect case is always more preferable for the content creators than the competition (see Figure 1.6 panel B). However, if the costs of platform’s investment are low, the content creators always prefers the competitive regime over the star effect regime (see Figure 1.5 panel B). The big content creators are the most inconsistent in their preferences – the star effect utility for them can be lower than the monopoly utility or higher than the competition utility depending on the platform’s cost of investment. In real terms, these costs are the opportunity cost of investing in a particular content creator versus investing into another one or selling this space to advertisers. It means that there are many similar content creators (the cost coefficient, c, is high), the content creators prefer to be in a competitive or in a star effect market. However, if there are only a few content creators, they prefer the monopoly over the star effect. 21 Figure 1.6: Equilibrium Utility and Profit as a function of initial number of viewers under different regimes. Parameters: k = 0.3; c = 0.5; ρ = 0.3; ¯e = 1. 1.6 Conclusion Westudytheplatform’sincentivestoinvestintocontentcreatorsunderdifferentcompetitive regimes in the market for content creators. We find that the platform has incentives to underinvest if there is some competition in the market. Moreover, the star effect reverses the investment dynamic in the market. Under monopoly and simple competition, the firm investment amount increases in the initial audience. However, under the star effect, the firm investment has an inverse u-shape in the initial number of viewers where the firm does not invest anything into really big content creators. The welfare implications of the regime change are uncertain. The consumer prefers the competitive regime over the monopoly, but the star effect can be more or less preferred to both of them. The firm prefers the monopoly to any competition as expected, but the preference of star effect over the simple competition depends on the model parameters. 22 Chapter 2 Consumer Inferences under Targeting: Implication for Pricing 2.1 Introduction Recent research finds that targeting can be effective in some situation. Goldfarb and Tucker (2011a) find by using data from almost 3,000 advertisement campaigns that targeting by matchingadstoawebsitecontent(contextualtargeting)increasespurchaseintentions. Gold- farb and Tucker (2011b) examine how privacy regulations impact effectiveness of online tar- geting. The authors use data from more than 3 million respondents who participated almost in ten thousand advertisement campaigns in the EU over a seven-year time period. They find that adoption of the EU privacy laws made advertisement 65% less efficient. Moreover, they find that for the same person an advertisement is more efficient in countries which have not implemented such laws. Later, Tucker (2014) finds that personalized and targeted ads are more efficient than non-targeted; moreover, when consumers think that they are not targeted they are almost twice more likely to click on a personalized and targeted ad. The latter result is quite impressive: when people have a false sense that they have privacy, they are more likely to react to persuasive ads. Rafieian and Yoganarasimhan (2019) find that an efficient targeting policy can improve the average click-through rate by more than 65% by using users’ behavioral information. However, these papers do not consider equilibrium con- 23 sequencesofconsumersknowledgeaboutbeingtargeted. Weareproposingamicromodelof consumerbeliefsunderdifferentprivacyregimestoconsidertheireffectonpricesandprofits. For example, consider a consumer who looked for a hotel for a vacation. She has two smallkidswhowillbetravellingwithher. Assumethatsheshopsonlineforbabyclothesand strollers. Advertiserscanusehercookiestoinferthatshehassmallkidsandshowherhotels with breakfast included because kids wake up early. Are these advertisements convincing? Probably, she will like them because they contain qualities which she needs. However, these advertisements would not be very persuasive because she knows that the advertiser knows herpreferencesandittailorsitsmessagetothem. Therefore,shewilldiscountthesemessages to some extent. Recently, privacy concerns have become an important topic for public policies. It is a result of controversies like Cambridge Analytica Facebook data leakage 1 or targeting of pregnant teenagers by Target 2 . Publicity of these stories increased internet users’ privacy concerns which lead to creation of more strict regulations in data collection and transferring processes. For example, the EU introduced General Data Protection Regulation (GDPR) in Mayof2018 3 andCaliforniaintroducedCaliforniaConsumerPrivacyAct(CCPA) 4 whichare aimed to increase consumer rights by giving them control over their information. Another goal of our paper is to use our model to predict potential consequences of new privacy regulations on prices, profits and consumer welfare. We develop a model in which a consumer seeks a good fit product. We assume that the firm can reach the consumer through an advertisement. This advertisement contains claims about the product that do not give any utility to the consumer, but they provide a signal about the fit. The firm can acquire a targeting technology to infer consumer preferences and adjust the message. We find that the consumer might discounts some of the new messages 1 The Cambridge Analytica Files. Retrieved from https://www.theguardian.com/news/series/cambridge- analytica-files 2 Charles Duhigg (2012, Ferbuary 16). How Companies Learn Your Secrets. Retrieved from https://www.nytimes.com/2012/02/19/magazine/shopping-habits.html 3 EUGDPR - Information Portal. Retrieved form https://eugdpr.org/ 4 Retrieved from https://oag.ca.gov/privacy/ccpa 24 when the firm uses the technology– he is willing topay less giventhe same receivedmessage when he is targeted. However, when we take the firm’s decision to set the price into the consideration, fourequilibriaemerge. Therearetwonon-targetedequilibria: inthefirstone, the firm sets a relatively high price and sells to the customers who receive a matching signal. In the second one, the firm she sets a relatively low price and serves the whole market. The second equilibrium emerge when the initial message is weak in revealing the product’s type. Then, we have two targeted equilibria. In the first one, the marketing message created with the use of thetechnology is more reveling about the true product’s type, and the firms sets a relatively high price and serves the customers who receive a matching signal. In the second one, the new message is vaguer than the initial one; therefore, the firm sets a relative low price and serves the whole market. 2.2 Literature Review In this section, we discuss relevant literature on persuasion and privacy. Our work is considering setting, in which firms are trying to influence consumer beliefs about a product fit by choosing an informational environment. Recent seminal paper by Kamenica and Gentzkow (2011) inspired a lot of new papers in economics of information in the recent years. In this paper, the authors show that a firm can persuade consumers to buy a product by optimally choosing an information environment. Their result relies on the assumption that the firm can commit to follow some disclosure policy which it chooses beforeobtainingtheinformationaboutstateoftheworld. ChakrabortyandHarbaugh(2014) used this idea to build a discrete choice model assuming the logistic distribution. Alonso and Cˆ amara (2016) considers the setting where a politician proposes a policy to voters. They find that, by using the voters’ heterogeneity, the politician can construct a policy that is implemented with probability one, but the voters are weakly worse-off compare to not implementing this policy. These papers show that an information design can be very 25 powerful in persuading people; however, they model their environments at a very high level. We are proposing a more micro-level model. Many papers in marketing and economics model optimal targeting in different environ- ment like TV/print media. Iyer et al. (2005) consider a case when firms observe different consumer groups within the market, and then they can choose to which group to advertise. They find that firms benefit from advertising to their followers, i.e., customers who have initial preference for the firm. Anand and Shachar (2009) examine advertising in a signal- ing model in which firms decide which media channel to choose to promote their product. They find that targeting in equilibrium can increase the amount of transmitted information compare to information contained in the advertisement itself through the strategic choice of the media. Johnson (2013) investigate a case in which consumers can avoid any messages by special software. He finds that targeting benefits firms even in this environment, but consumers and society can be worse off. Spiegel (2013) considers a trade-off between pri- vacy and targeting in software and the adware market. The author compares conditions in which it is more profitable to issue a product as a commercial software that provides a full privacy or to issue a product as an adware that collects information about consumers and shows them advertising based on it. Gardete and Bart (2018) use cheap-talk environment to examine how market outcomes change under different privacy levels. Shin and Yu (2019) build a model in which firms compete for consumers who are looking for a fitting product. They find that targeting always increases consumer’s beliefs about the product fit – in our model, we find that the opposite result can happen sometimes. Another stream of literature considers under which conditions privacy can be socially optimal. Corniere and Nijs (2016) model competition for advertisement slots in which a platform can provide advertisers with information about consumers. They find that disclos- ing information improves the matching between advertisers and consumers, but it leads to price increase even without price discrimination. Cummings et al. (2016) examine the possi- bilitytoempiricallylearnconsumer preferenceswhenconsumershaveprivacyconcerns. The 26 authors use revealed preference theory and they find that under a very strict assumptions about consumers’ utilities, it might be impossible to infer their preferences. Gradwohl and Smorodinsky (2017) formalize a new type of games, perception games, in which consumers can have privacy concerns. Dimakopoulos and Sudaric (2018) consider a platform compe- tition in which platforms collect consumer information to improve targeting. They assume that consumers incur privacy cost and they find that there exist conditions under which platforms collect a socially optimal level of consumer information. 2.3 Model 2.3.1 Setup Therearetwoplayers: afirm(she)andacustomer(he). Thefirmsellsherproductatprice p. To sell the product, the firm advertises it through the internet advertisement. The customer seeks the product that has a good fit to him. Here, we consider the context where the consumer cannot observe the fit directly before the consumption, but he can observe claims about the product which give a noisy signal about the fit. These claims can be statements about the product attributes; however, they do not provide any utility by themselves. This means that even if all claims are appealing to the consumer, he still might not like the product because of unobservable factors. Weassumethefollowingstructureofthegame. Thefirmcanbeoftwotypes: θ ∈{0,1}, where P(θ = 0) = P(θ = 1) = 0.5. We assume that the products have a similar quality, and the only thing that matters is the fit between the customer and the product. The firm observes its type in the beginning of the game, but she does not know the type of the customer. The customer can be of two types: t∈{0,1}, where P(t = 0) = P(t = 1) = 0.5. We define the product to be a good fit if the type of the firm and the type of the customer match. The customer cannot observe the type of the firm before the consumption. He receivesanoisysignalaboutthefirm’stypethroughtheinternetadvertising. Weassumethat 27 the signal has the following structure: s∈{0,1}, P(s = 1|θ = 1) = P(s = 0|θ = 0) = g, and P(s = 1|θ = 0)=P(s = 0|θ = 1)= 1− g. This means that the customer has a higher probability to receive a signal that matches the firm’s true type. Weassumethatthefirmcreatesthemessageusingthegenericdescriptionoftheproduct; therefore, it reveals the fit to some degree, but not perfectly. In our set-up, the firm always sends a message to the consumer because otherwise the customer does not know that the product exists. The firm can purchase a targeting technology, τ ∈{0,1}, that discovers the customer’s type for the firm. The cost of the targeting technology is c τ > 0. The customer knows whether the firm purchased the technology by seeing the request to use his cookies upon entering a website. This technology also allows to study the customers’ preferences about the information representation to further tailor the message. In particular, it can help to increase the chance that the message will be understood correctly. We formalize it in the following way. The firm can make a marketing action, a ∈ {0,1}, that costs c a > 0. Thisactionconsistsofstudyingthecustomerinformationfromthetargetingtechnologyand improving the message about the product type. In particular, it changes the probability of the matching signal by modifying the signal structure: P(s = 1|θ = 1)=P(s = 0|θ = 0)= m, and P(s = 1|θ = 0) = P(s = 1|θ = 0) = 1− m, where m > 0.5. The customer cannot learn whether the firm used his information to change the message. If the firm does not have the technology, it does not have access to the customers’ data to modify the message. Therefore, we assume that the firm cannot make a marketing action without having the technology. Timing of the game: 1. The firms starts production and observes its type. 2. The firm sets a price. 3. Thefirmdecideswhethertobuyatargetingtechnology. Ifthefirmhasthetechnology, it observes the type of the consumer. 28 4. Based on this information, the firm decides whether to make a marketing action. 5. The consumer observes the firm’s message and decides whether to buy or not. 2.3.2 Customer problem The risk-neutral customer visits a website and observes the advertisement provided by the firm. He also observes if the firm uses his cookies, but he does not know whether she uses it to change the advertising message or not. We assume that the customer receives utility of one when the product is a good match forhim. Ifthecustomerdoesnotpurchasetheproduct, hereceivesautilityof0. Theutility from the purchase has the following von Neumann–Morgenstern form: U =I{good fit product }− p (2.1) The customer observes whether the firm uses the targeting technology and the received signal, s. Based on this information, the customer makes an inference about the firm’s type using the Bayes rule. The belief of type t customer that the firm’s type matches given the signal, s, and given the firm’s use of the targeting technology, τ , is: µ (θ = t|s,τ ). The expected utility for the customer under this belief is: E[U|p,t,s,τ ] =µ (θ =t|s,τ )· 1− p (2.2) If the expected utility is at least zero, the customer purchases the product. Otherwise, he enjoys the utility of zero from the outside option. 2.3.3 Firm problem Therisk-neutralfirminheritstheproductionoftheproductoftype θ ∈{0,1}. Thefirmsets the price, p, at which she sells to anyone who is willing to buy the product. The firm has the advertising message that was created based on the product characteristics. The product is 29 experiential in nature; therefore, the customer cannot perfectly deduce whether it is a good fit for him from the message. However, the message is informative in a sense that customer correctly infers the true type with probability g > 0.5. The customer is not aware about the firm’s existence in the beginning of the game. The firm sends the message to let him know about the product existence. The firm can purchase a targeting technology, τ , that allows to learn the customer’s preferences. In particular, it allows the firm to understand how the customer analyzes information to create a new message. The technology costs c τ which is paid upon the acquisition. If the firm wants to change the message, s, she has to incur additional costs, c a . This acquisition allows the firm to change the probability that the customer understands the message correctly. If the firm makes this marketing action, the customer correctly understands the firm’s type with probability m. The firm then faces a choice – to which customer’s types to change the message if any. We denote this action as a(t)∈{0,1} that is equal to 1 if the firm changes the message to type t. Whenthecustomerreceivesthemessage, heobserveswhetherthefirmusesthetargeting technology. However, he does not know whether the firm uses this information to change the message for his type. Given the message and the information about the targeting, he decides whether to buy the product or not. The firm has the following profit function: E[π (a(· )|p,τ,θ = 0)]= =p X i∈{0,1} P(t =i) X j∈{0,1} P(s =j|θ = 0,a(i))· I{µ (θ = 0|s =j,τ )≥ p}− − c τ · I{purchase technology}− c a · I{mkt action} (2.3) We find all pure strategy equilibria in the following sections. 30 2.4 Strategies We start our analysis with deriving the strategies that can be sustained in an equilibrium. Wefindconsumer’sconsistentbeliefsforallpossiblefirm’spurestrategyequilibriumactions. For the out of equilibrium beliefs, we assume the following behavior for the customer: Assumption 1. The customer uses the same the prior distribution of the firm’s types if he sees an out of equilibrium price. This assumption comes from the symmetry of the game. The customer does not have a good reason to believe that one firm type has higher propensity to deviate that the other. Therefore, he assumes that this deviation is equally likely to be done by each firm’s type. After finding the beliefs, we compute the firm’s profit given these beliefs. We proceed with the solution in the following way: first, we consider the payoffs for optimal strategies under no targeting; then, we find payoffs for the targeting case. Finally, we find equilibria of this game. 2.4.1 No technology When the firm does not have the targeting technology, she relies on the message that she already has. The customer observes that the firm does not have the targeting technology. Let us find the belief of the customer about the firm’s type upon receiving signal 0. This signal can be received from the firm type 0 with probability g or from the firm type 1 with probability 1− g. Therefore, using the Bayes formula, we obtain the following belief: µ (θ = 0|τ = 0,s = 0)= 0.5g 0.5g+0.5(1− g) =g (2.4) Using the same logic, we obtain the belief of the customer upon receiving signal 1: µ (θ = 0|τ = 0,s = 1)= 0.5(1− g) 0.5g+0.5(1− g) = 1− g (2.5) 31 Pricing. The firm knows the customer’s beliefs. There are only two prices that are optimal for the firm to consider: the highest price when the customer buys upon receiving a matching signal (p = g), and the highest price when the customer buys upon receiving a negative signal (p = 1− g). If the firm sets a price that is a bit higher, she does not sell anything if the price is relatively high, or she losses half of the market with only a small gain in price. Therefore, the firm does not set a price that is higher than the proposed prices. It is also not profitable to set a lower price because it does not increase the market share. Let us compute the profits when the firm serves the “match” segment and when it serves the whole market. Serve the matching customers. The firm sets a relatively high price, p = g, and serves the customers that receive a matching signal. The expected profit is: E[π p h (a = 0|θ = 0,τ = 0)]=g 0.5g+0.5(1− g) = 0.5g (2.6) The expected profit increases in the precision of the signal. The higher the precision, the higher the willingness to pay upon receiving a good signal, so the firm can set a higher price. Serve the whole market. The firm sets a relatively low price, p = 1− g, and serves all customers. The expected profit is: E[π p h (a = 0|θ = 0,τ = 0)]= (1− g) 0.5· 1+0.5· 1 = 1− g (2.7) The expected profit decreases in the precision of the signal. The higher the precision of the signal, the lower the willingness to pay upon receiving a bad signal. When the customer receives a bad signal in this case, he has higher certainty in the fact the firm is not a good match for him. Therefore, the firm have to set a lower price to serve the whole market. 2.4.2 Technology The firm purchases the targeting technology. The customer observes that the firm uses the targeting technology, but he cannot observe whether the firm uses this technology to change 32 thesignaldistribution. Weconsidertheconsumer’sbeliefsthatareconsistentwiththefirm’s pure strategies. To simplify the notation, we denote a m the action for the firm to change the messagedistributionforthematchingtype,anda n tochangethemessagedistributionforthe non-matching type. Now, the firm’s action space expands to ( τ,p,a m ,a n ). Let us consider thecustomer’sconsistentbeliefsandtheoptimalpricesforallfourpossiblemarketingaction pairs, (a m ,a n ): Usethetechnologyforeveryone. Inthiscase,thefirmchangesthesignaldistribution for all customer, i.e., (a m = 1,a n = 1). The customer’s belief upon receiving signal 0: µ (θ = 0|τ = 1,a m = 1,a n = 1,s = 0) = 0.5m 0.5m+0.5(1− m) =m (2.8) We receive a similar result to the non-targeting case – the customer’s belief is increasing in the precision of the signal. The customer’s belief upon receiving signal 1: µ (θ = 0|τ = 1,a m = 1,a n = 1,s = 1)= 0.5(1− m) 0.5m+0.5(1− m) = 1− m (2.9) The price decreases in the precision of the signal. Using the same logic as in the non- targeting case, there are only two prices to consider. The firm’s profit when it serves only the matching customers, i.e., p =m: E[π p h (a m = 1,a n = 1|θ = 0,τ = 0)]=m 0.5m+0.5(1− m) − c m − c τ = = 0.5m− c m − c τ (2.10) We get a similar result to the no technology case because the only thing that changes is the signal distribution. The firm’s profit when it serves the whole market, i.e., p = 1− m: E[π p l (a m = 1,a n = 1|θ = 0,τ = 0)]= (1− m) 0.5· 1+0.5· 1 − c m − c τ = = 1− m− c m − c τ (2.11) 33 Usethetechnologytotargetagoodmatch. Thefirmchangesthesignaldistribution onlytothematchingtype,i.e.,(a m = 1,a n = 0). Thecustomer’sbeliefuponreceivingsignal 0: µ (θ = 0|τ = 1,a m = 1,a n = 0,s = 0)= 0.5m 0.5m+0.5(1− g) = m m+(1− g) (2.12) Thebeliefincreasesbothintheprecisionofthemarketingmessageandtheoriginalmessage. It increases in the precision of the new signal because the matching type sees the correct type with higher probability. It increases in the original message because when it is not a match, the customer sees it with higher probability. The customer’s belief upon receiving signal 1: µ (θ = 0|τ = 1,a m = 1,a n = 0,s = 1)= 0.5(1− m) 0.5(1− m)+0.5g = 1− m 1− m+g (2.13) This belief decreases both in the original message and in the marketing message. Again, there are only two price points to consider. The firm’s profit when it serves the customers who received a good match signal, i.e., p = m m+(1− g) : E[π p h (a m = 1,a n = 0|θ = 0,τ = 1)]= m m+(1− g) 0.5m+0.5(1− g) − c m − c τ = = 0.5m− c m − c τ (2.14) The price looks a bit complicated, but the profit is exactly the same as in the previous case when the firm changes the message to everyone. This follows from the fact that the price change compensates by the demand change, e.g., if the price decreases, the demand increases in the way that the revenue stays the same. The firm’s profit when it serves the whole market, i.e., p = 1− m 1− m+g : E[π p l (a m = 1,a n = 0|θ = 0,τ = 1)]= 1− m 1− m+g 0.5· 1+0.5· 1 − c m − c τ = = 1− m 1− m+g − c m − c τ (2.15) 34 The firm serves the whole market, so the profit moves the same direction as the price does when precisions of the signals change. When precision of the targeting signal increases, the matchingtypeknowsthatwhenheseesabadsignal, itisanon-matchwithhighprobability. Usethetechnologytotargetabadmatch. Thefirmchangesthesignaldistribution to the non-match type, i.e., (a m = 0,a n = 1). The customer’s belief upon receiving signal 0: µ (θ = 0|τ = 1,a m = 0,a n = 1,s = 0)= 0.5g 0.5g+0.5(1− m) = g g+(1− m) (2.16) The belief is increasing in the both signals. The customer’s belief upon receiving signal 1: µ (θ = 0|τ = 1,a m = 0,a n = 1,s = 1)= 0.5(1− g) 0.5(1− g)+0.5m = 1− g 1− g+m (2.17) This belief is decreasing in the signals. We consider the two price points for the firm. The firm’s profit when it serves only the matching segment, i.e., p = g g+(1− m) : π p h (a m = 0,a n = 1|θ = 0,τ = 0)= g g+(1− m) 0.5g+0.5(1− m) − c m − c τ = = 0.5g− c m − c τ (2.18) The revenue is the same as in the non-targeted case serving the matching type, but the costs are higher. The firm’s profit when it serves the whole market, i.e., p = 1− g 1− g+m : E[π p l (a m = 0,a n = 1|θ = 0,τ = 0)]= 1− g 1− g+m 0.5· 1+0.5· 1 − c m − c τ = = 1− g 1− g+m − c m − c τ (2.19) The profit decreases in both signal precisions. Do not use the technology to target. In this case, the firm purchases the targeted technology, but does not use it change the signal distribution, i.e., (a m = 0,a n = 0). All beliefs and prices are the same as in the non-targeted case. The customer’s belief upon receiving signal 0: µ (θ = 0|τ = 1,a m = 0,a n = 0,s = 0)=g (2.20) 35 The customer’s belief upon receiving signal 1: µ (θ = 0|τ = 1,a m = 0,a n = 0,s = 1)= 1− g (2.21) Thefirm’sprofitwhenitservesthecustomerswhoreceivedamatchingsignal, i.e., p =g: E[π p h (a m = 0,a n = 0|θ = 0,τ = 0)]= 0.5g− c τ (2.22) The firm’s profit when it serves the whole market, i.e., p = 1− g: E[π p l (a m = 0,a n = 0|θ = 0,τ = 0)]= 1− g− c τ (2.23) The only difference with the non-targeting case is that the firm has to pay the technology cost, c τ . 2.5 Equilibria We are looking for symmetric firm-preferred pure strategy subgame perfect equilibria of this game. We solve this game backwards. First, we fix all the firm’s actions (price, targeting technology and marketing actions) to find the customer’s inference about the firm’s type given the firm’s choices. Then, we compute the firm’s profit under all possible marketing actions, targeting choice, and prices. Finally, we find strategies that can be sustained in the equilibrium. We are looking for symmetric equilibria; therefore, the price does not signal the type. Given the symmetry of the problem, we only need to consider a single firm type and the result will be the same for the other type. We analyze type 0 firm’s problem. The firm has 10 strategy profiles that might be sustained in equilibria. We write them in Table 2.1. We will split the analysis in three parts. First, we will consider the marketing messages that improve the quality of the signal, i.e., m > g. Then, we will consider the information reduction signals m < g. In particular, we consider two cases: when the firm 36 has to incur some cost to create this message and when the firm can costlessly create the message that reduces the information. Table 2.1: Firm’s payoffs and customer’s beliefs. # p τ a m a n µ π 1 g 0 0 0 g 0.5g 2 1− g 0 0 0 1− g 1− g 3 m 1 1 1 m 0.5m− c τ − c a 4 1− m 1 1 1 1− m 1− m− c τ − c a 5 m m+(1− g) 1 1 0 m m+(1− g) 0.5m− c τ − c a 6 1− m 1− m+g 1 1 0 1− m 1− m+g 1− m 1− m+g − c τ − c a 7 g g+(1− m) 1 0 1 g g+(1− m) 0.5g− c τ − c a 8 1− g 1− g+m 1 0 1 1− g 1− g+m 1− g 1− g+m − c τ − c a 9 g 1 0 0 g 0.5g− c τ 10 1− g 1 0 0 1− g 1− g− c τ 2.5.1 Information improving marketing message Inthissection,werestrictourattentiontothemarketingmessageswherem>g. Inthiscase, the new message provides the correct signal about the firm’s type with higher probability than the standard signal. In the following proposition we show that there are only three equilibria are possible in this case. Proposition 2. There are three equilibria in this case. 1. The firm does not target ( τ = 0), sets relatively high price, p = g, and customer buys when he sees a matching message to his type. 2. The firm does not target ( τ = 0), sets relatively low price, p = 1− g, and the customer always buys. 37 3. The firm targets ( τ = 1), sets relatively high price, p = m m+(1− g) , sends marketed message to the match type (a m = 1) and non-marketed message to the non-match type (a n = 0). The customer buys when he sees a matching message to his type. See the formal proof in the Appendix. Here, we provide some intuition behind how we eliminate not equilibrium strategies. First, we eliminate all targeting strategies where the firm sets a relatively low prices, i.e., she sells to all customers. These strategies are dominated by non-targeting and selling to the whole market. If the firm targets, she incurs thetargetingtechnologycostsand/ormarketingmessagecosts. Atthesame, theconsumer’s beliefs reduce when the firm serves the whole market, so she can only charge a lower price. Therefore, the demand stays constant, the price reduces, and the cost is higher, so the firm preferstodeviatetonon-targeting. Whenthefirmpurchasethetechnology,butdoesnotuse it,sheincurscostswiththesamerevenue,soshedoesnotdoit. Whenthefirmpurchasesthe technology and uses it to change the message to both types, she receives the same payoff as changing the signal only to the matching type (see 3 and 5 in Table 2.1). If the firm deviates from changing message to both types to only change the message to the matching type, the demand increases; therefore, she prefers to deviate. Finally, changing the signal distribution only to the non-matching type provides the same revenue as non-targeting and high price, but it creates extra costs, so the firm deviates. We are left with only three strategies: low price and non-targeting, high price and non-targeting, and high price and targeting with changing the message only to the matching type (a m = 1,a n = 0). 38 Figure 2.1: Equilibria when c τ = 0.04, c a = 0.01. The border between low and high price non-targeting equilibrium lies at g = 2/3. If the initial message has low informativeness (g < 2/3), the firm prefers to serve the whole market and set a relatively low price. However, if the message is decently informative (g > 2/3), the firm would prefer high price and the customer who perceives the product to be a good fit to serving the whole market. If we plot g− m axes, the targeting high price equilibrium wedges between these two equilibria. We plot this in g− m axes in Figure 2.1. However, the targeting equilibrium does not always exist. First, if the costs of targeting are too high (c tau +c a > 1 6 ), the firm prefers not to target. High costs make the technology purchase too expensive, so the increased revenue does not cover it. Moreover, the firm might prefer to deviate to not creating a new message. In this case, the customer has a strong belief that the product is a good fit when he receives a matching signal, so the firm has incentives to not create a new message, save costs, enjoy a high price that overweight the loss in the demand caused by a weaker (standard) signal. The firm chooses this scenario when the ratio of creating new message cost to targeting technology is sufficiently high. However, when it 39 is a bit lower, the triangle loses some of the lower part (see Figure 2.2), but the targeting equilibrium still exists for some parameters. Figure 2.2: Equilibria when c τ = 0.02, c a = 0.08. Thetargetingequilibriumwedgesbetweennotargetinglowandhighpriceequilibria, but for some cost parameters it might lead to non-linearities in g. The equilibria are monotonic when we vary m. When we increase m, a non-targeting equilibrium (either low- or high- price) might change to the targeted high price equilibria. When the full triangle exists, i.e., the firm’s incentives to deviate are pretty low, the price dynamic is non-linear, but not that much. When m is sufficiently high, and when we increase g from 0.5 to 1, we first have the non-targeting equilibrium with a relatively low price, then the firm moves to the targeting equilibrium with the high price. Finally, if we increase g more, the firm prefers the non-targeting and a relatively high price. This price is actually lower than the targeted price, so we have increase and then decrease in the price. It appears because when the initial message is not too good, the firm benefits a lot when it starts to use the targeting technology. However, when the initial message becomes better (i.e., g increases), the benefit 40 from the new message decreases; therefore, the firm prefers to serve the customer with the perceived matching signal. When the part of the triangle is “cut” because the firm prefers to deviate, we obtain the equilibria depicted in Figure 2.2. Most of the dynamic remains the same. However, there is a case when the price shows even higher non-linearity. When we increase the precision of the initial message, g, from 0.5 the price first increases, but then it returns to the initial value, and then it increases again. It happens because the firm cannot reliably commit to the high price targeting strategy, so it would deviate to non-targeting in cases when there is exist a higher payoff under the targeting. 2.5.2 Costly information reduction marketing message We consider marketing messages that reduce the information in the signal, i.e. m < g. In this case, when the firm implements the targeting technology, it contaminates the message with vague information that prevents customers to understand the firm’s type. Moreover, we assume that the firm cannot cheaply create the new message. The payoffs are exactly the sameasinthepreviouscase,buttheirorderisdifferentbecauseoftheassumptiononquality of the new message. Given this assumption, the firm will not use the targeting technology. Proposition 3. There are two equilibria in this case. 1. The firm does not target ( τ = 0), sets relatively high price, p = g, and customer buys when he sees a matching message to his type. 2. The firm does not target ( τ = 0), sets relatively low price, p = 1− g, and the customer always buys. There are only non-targeting equilibria in this case. The targeting technology reduces the precision of the signal; therefore, the customer’s belief that the product is a good fit for him upon receiving a matching signal decreases compared to the standard message. As a result, all the high prices strategies have lower prices than in the non-targeting case and higher costs and the possible increase in the demand does not cover this difference. For 41 the low prices, i.e., when the firm serves the whole market, she can set higher prices than in the non-targeting case. Therefore, it seems that it might be profitable for the firm to target and set relatively low price when the increase in the price covers the costs. However, these strategies cannot be equilibrium strategies because the firm has incentive to deviate to non-creation of the new message because it reduces the costs and the demand and price stay the same. Therefore, there are no targeting equilibrium in this case. 2.5.3 Costless information reduction marketing message This section looks like the previous section, i.e. m < g, but now the creation of the new marketing message is free (”cheap”), i.e. c a = 0. The firm has incentives to contaminate the message to reduce the information when the customer receives a non-matching signal. This would lead to higher willingness to pay and thus a higher price while serving the whole market. the following proposition defines the equilibrium types in this scenario. Proposition 4. There are three equilibria in this case. 1. The firm does not target ( τ = 0), sets relatively high price, p = g, and customer buys when he sees a matching message to his type. 2. The firm does not target ( τ = 0), sets relatively low price, p = 1− g, and the customer always buys. 3. The firm targets ( τ = 1), sets relatively low price, p = 1− m, sends marketed message to both type (a m = 1,a n = 0). Customer always buys. To receive this result, we invoke the fact that we are looking for the firm’s-preferred equilibria. The high-price strategies are not equilibria by the same reasoning as in the previoussection, butthelow-pricestrategieswhenthefirmchangesthemessageareallNash equilibria. However, they provide different profits to the firm, so we restrict the equilibrium onlytotheonethatprovidesthehighestpayoff. Inthiscase, itwillbethestrategywhenthe 42 firm changes the signal to both types ( a m = 1,a n = 1). This strategy generates the highest belief that the product is a good for the customer when he receives a non-matching signal. Figure 2.3: Equilibria when c τ = 0.05, c a = 0. The targeting equilibrium again wedges between low and high non-targeting equilibria. We observe the reverse dynamic in precision of the new signal – when we increase it, the targeting equilibrium switches to the non-targeted equilibria. Moreover, when we increase the precision of the initial signal, the price is monotonic. First, it increases from the low non-targeted price to the low targeted price. Then, it increases even higher to the high non-targeted price. This equilibrium shift happens because when the precision of the initial signalincreases,thebeliefthattheproductisagoodfituponreceivinganon-matchingsignal decreases. The targeting message provides a higher belief upon receiving a non-matching signal and the costs are not too high, so the firm decides to use the technology. However, as theprecisionoftheinitialsignalgrowsfurther, itbecomesmoreviabletoservethecustomer with perceived matching message setting a high price. 43 2.6 Conclusion Westudytheequilibriumeffectsofthetargetingontheconsumerinferenceabouttheproduct inferred fit and on the prices. We find that there are four equilibria possible in this model. There are two non-targeted equilibria: depending on precision of the initial signal the firm sets relatively high or low price and sets part or the whole market. 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Let us find the first order condition for the profit: ∂Π( i,e) ∂i =− 2ci+0.5v 1 − k((1− λ )v 1 +2λ (1+i+e)v 2 1 ) 2 = 0 Now, let us check whether that it is a maximum: ∂ 2 Π( i,e) ∂i 2 =− 2c− kλv 2 1 < 0 The second order condition is always negative for the model parameters; therefore, it is indeed the maximum. Now, let us find the first order condition for the utility function: ∂U(i,e) ∂e =− 2ρe +0.5v 1 + k((1− λ )v 1 +2λ (1+i+e)v 2 1 ) 2 = 0.5v 1 + k((1− λ )v 1 +2λ (1+i)v 2 1 ) 2 +(kλv 2 1 − 2ρ )e = 0 Let us check whether it is a maximum: ∂ 2 U(i,e) ∂e 2 =− 2ρ +kλv 2 1 Thisexpressioncanbothpositiveandnegative. Ifv 2 1 < 2ρ kλ , itisnegative,andthesolutionis indeedthemaximum. However,whenv 2 1 > 2ρ kλ ,thefirstordersolutionprovidestheminimum of the function. The first derivative is increasing in this region and the term without effort 49 is always positive meaning that the utility function is increasing in effort. Therefore, the maximum lies on the border of e for this parameter region, e br = ¯e. Now, let us include the restriction on effort and investment into the best response func- tion: e br (i;· ) = = min v 1 (1+k(1− λ ))+2kλv 2 1 4ρ − 2kλv 2 1 + 2kλv 2 1 4ρ − 2kλv 2 1 max{0,i}, ¯e , if v 2 1 < 2ρ kλ ¯e, if v 2 1 ≥ 2ρ kλ i br (e;· ) = max v 1 (1− k(1− λ ))− 2kλv 2 1 4c+2kλv 2 1 − 2kλv 2 1 4c+2kλv 2 1 min{e,¯e}, 0 Lemma1. Uniquenessofintersectionofthebestresponsefunctions in the star effect case. Let us denote a = v 1 (1+k(1− λ ))+2kλv 2 1 4ρ − 2kλv 2 1 and b = 2kλv 2 1 4ρ − 2kλv 2 1 , then e br (i;· ) = min a+ bmax{0,i}, ¯e . a≥ 0 and b≥ 0 in the interior range; therefore, e br (i;· ) is either initially increasing and then equals to ¯e 5 or equals ¯e for all i≥ 0. Let us denote c = v 1 (1− k(1− λ ))− 2kλv 2 1 4c+2kλv 2 1 and d = 2kλv 2 1 4c+2kλv 2 1 , then i br (e;· ) = max c− dmin{e,¯e}, 0 . c can be both positive or negative, while d > 0. If c− d¯e > 0, then i br (e;· ) decreases until ¯e and then equals to c− d¯e; otherwise i br (e;· ) decreases until c/d and then equals to 0. See Figure A.1 for graphical representation of the cases. e br (i;· ) and i br (e;· ) are weakly monotonic continuous functions that consist of linear splines. They cannot have more than one intersection because e br (i;· ) is weakly increasing in i and i br (e;· ) is weakly decreasing in e. Let us show that e br (i;· ) and i br (e;· ) always intersect. These functions do not have inverse functions because they are not injective; therefore, we have to argue in terms of the function domains and ranges of the functions. e br (i;· ) continuously weakly increases in i, ran(e br ) = [a,¯e]⊂ (0,¯e] and dom(e br ) = (0,∞). 5 e br =a when i≤ 0; e br =a+bi for i∈ (0, e− a d ; e br = ¯e for i> e− a d ) 50 0.5 1 1.5 2 2.5 3 −0.2 0.2 0.4 0.6 0.8 1 1.2 1.4 ( ¯ e−a b , ¯ e) (0,a) Investment Effort S-shaped e br e br = ¯ e 0.5 1 1.5 2 −0.2 0.2 0.4 0.6 0.8 1 1.2 ( c d , 0) (¯ e,c−d¯ e) Effort Investment i br (case 1) i br (case 2) Figure A.1: Best response functions. i br (e;· ) continuously weakly decreases in e on [0,¯e] and ran(i br ) = [0,max{0,c}]; therefore, they intersect in this region. Proof of Proposition 1 Wesolvethesystemofthebestresponseequationsbyfirstrelaxingthemin /maxconditions and finding the interior solution of the relaxed system of equations. Then we find the best responses to the corner solutions on effort/investment. The interior solution of the investment/effort maximization is: e i (· ) = (v 1 (1+k(1− λ ))+2kλv 2 1 )(4c+2kλv 2 1 )+2kλv 2 1 (v 1 (1− k(1− λ ))− 2kλv 2 1 ) (4ρ − 2kλv 2 1 )(4c+2kλv 2 1 )+(2kλv 2 1 ) 2 i i (· ) = (v 1 (1− k(1− λ ))− 2kλv 2 1 )(4ρ − 2kλv 2 1 )− 2kλv 2 1 (v 1 (1+k(1− λ ))+2kλv 2 1 ) (4ρ − 2kλv 2 1 )(4c+2kλv 2 1 )+(2kλv 2 1 ) 2 The corner solutions are the following. e b ≡ e br (i = 0;· ) = v 1 (1+k(1− λ ))+2kλv 2 1 4ρ − 2kλv 2 1 i b ≡ e br (e = ¯e;· ) = v 1 (1− k(1− λ ))− 2kλv 2 1 (1+¯e) 4c+2kλv 2 1 1. To obtain these results, we substitute monopoly (k = 0) and competitive (λ = 0) parameters into equations 1.5 and 1.6. 51 Figure A.2: Intersection of the best response functions. Parameters: Panel A: k = 0.3; c = 0.3; ρ = 0.3; ¯e = 1; v 1 = 0.5. Panel B: k = 0.3; c = 0.2; ρ = 0.4; ¯e = 1; v 1 = 0.7. Panel C: k = 0.3; c = 0.2; ρ = 0.23; ¯e = 1; v 1 = 0.5. Panel D: k = 0.5; c = 0.7; ρ = 0.2; ¯e = 1; v 1 = 0.7 2. There are only four possible equilibrium outcomes to consider: (i ∗ ,e ∗ ), (i b ,¯e), (0,e b ) and (0,¯e). Next, we derive properties of the boundary and interior solutions. Both e b (· ) and e i (· ) are derived from e br (· ). They are the same at i = 0. e br (· ) is increasing in i, so for positive values of i, e i (· ) > e b (· ). Conversely, for negative values of i, e i (· )<e b (· ). Similarly, i b (· ) and i i (· ) are derived from i br (· ), and they are the same at e = ¯e. Moreover, i br (· ) is decreasing in e, so for values of e < ¯e, e i (· ) > e i (· ) and for e> ¯e, e i (· )<e i (· ). Therefore, the following properties hold in equilibrium a) i i (· )> 0 ⇒ e i (· )>e b (· ); b) i i (· )< 0 ⇒ e i (· )<e b (· ); c) e i (· )> ¯e ⇒ i b (· )>i i (· ); d) e i (· )< ¯e ⇒ i i (· )>i b (· ). 52 a. The intersection of the best responses is in the interior region; therefore, the solution is indeed interior. b. – Ife b (· )≥ ¯e&i i (· )≤ 0. Sincei i (· )≤ 0,theequilibriumcannotbeinterior. We cannot have zero investment and boundary effort because e b (· )≥ ¯e. Possible outcomes under these parameters are: e ∗ = ¯e & i ∗ = max{i b ,0}. – If e b (· ) < ¯e & i i (· ) > 0. By i i (· ) > 0, we cannot have zero investment and boundary effort. By property (a), we can have ( e ∗ = ¯e & i ∗ = i b ). (e ∗ =e i & i ∗ =i i ) is also possible under these restrictions. – If e b (· ) ≥ ¯e & i i (· ) > 0. By property (a), the only possible outcome is: e ∗ = ¯e & i ∗ =i b . c. – If e i (· ) < ¯e & i b (· ) > 0. By property (d), the optimal investment should be positive under these restrictions. Therefore, the only possible outcome is interior: e ∗ =e i & i ∗ =i i . – If e i (· ) ≥ ¯e & i b (· ) ≤ 0. By property (b), the only possible outcome is: e ∗ = ¯e & i ∗ = 0. – If e i (· ) < ¯e & i b (· ) ≤ 0. By property (d), we can have either the interior solution or zero investment and boundary effort: ( e ∗ = e i & i ∗ = i i ) or (e ∗ =e b & i ∗ = 0). d. – If e b (· ) < ¯e & i b (· ) ≤ 0. We cannot have the case when effort is at the maximum and the investment is boundary because i b (· ) ≤ 0. The other cases with positive effort are possible under this conditions, so the potential outcomes are: either (e ∗ =e i & i ∗ =i i ) or (e ∗ =e b & i ∗ = 0). – Ife b (· )≥ ¯e&i b (· )> 0. Byproperty(a), wecannothavetheinteriorsolution. The only possible outcome is: e ∗ = ¯e & i ∗ =i b . 53 – If e b (· )< ¯e & i b (· )> 0. The only impossible scenario is when the investment iszerobecausei b (· )> 0. Thepossibleoutcomecanbeoneoftheseremaining options: (e ∗ =e i & i ∗ =i i ) or (e ∗ =e b & i ∗ = 0) or (e ∗ = ¯e & i ∗ =i b ). There are only four feasible equilibrium effort and investment pairs: ( i ∗ ,e ∗ ), (i b ,¯e), (0,e b )and(0,¯e). Weseethatthealternativeconditionsleadtootherpossibleoutcomes than the letter prescribes. Therefore, our restrictions on the parameters describe the equilibrium outcomes for all parameter values. 3. We demonstrated the proof in the Negotiation subsection. Proof of Corollary 1 1. Let us show that the monopoly investments are higher than the competitive case: i ∗ m − i ∗ c = v 1 4c − v 1 (1− k) 4c = kv 1 4c > 0 2. Let us show that the monopoly investments are higher than the star effect boundary case: i ∗ m − i b = v 1 4c − v 1 (1− k(1− λ ))− 2kλv 2 1 (1+¯e) 4c+2kλv 2 1 = = v 1 (4c+2kλv 2 1 )− 4c(v 1 (1− k(1− λ ))− 2kλv 2 1 (1+¯e)) 4c(4c+2kλv 2 1 ) = = 2kλv 3 1 +4ck(1− λ )v 1 +8ckλv 2 1 (1+¯e) 4c(4c+2kλv 2 1 ) > 0 3. Let us show that the monopoly investments are higher than the star effect boundary case: i ∗ m − i i = v 1 4c − (v 1 (1− k(1− λ ))− 2kλv 2 1 )(4ρ − 2kλv 2 1 )− 2kλv 2 1 (v 1 (1+k(1− λ ))+2kλv 2 1 ) (4ρ − 2kλv 2 1 )(4c+2kλv 2 1 )+(2kλv 2 1 ) 2 54 The combined fraction is too big, so we study it by parts. The denominator has the following form: 4c((4ρ − 2kλv 2 1 )(4c+2kλv 2 1 )+(2kλv 2 1 ) 2 ) 4ρ − 2kλv 2 1 > 0 in the interior region and the denominator is always positive. Let us simplify the numerator: v 1 ((4ρ − 2kλv 2 1 )(4c+2kλv 2 1 )+(2kλv 2 1 ) 2 )− 4c((v 1 (1− k(1− λ ))− 2kλv 2 1 )(4ρ − 2kλv 2 1 )− − 2kλv 2 1 (v 1 (1+k(1− λ )+2kλv 2 1 )) =v 1 (4ρ − 2kλv 2 1 )4c+v 1 ((4ρ − 2kλv 2 1 )(2kλv 2 1 +v 1 (2kλv 2 1 ) 2 )− − 4cv 1 (4ρ − 2kλv 2 1 )+4c(v 1 k(1− λ )+2kλv 2 1 )(4ρ − 2kλv 2 1 )+2kλv 2 1 (v 1 (1+k(1− λ ))+2kλv 2 1 )) = =v 1 ((4ρ − 2kλv 2 1 )(2kλv 2 1 +v 1 (2kλv 2 1 ) 2 )+ +4c(v 1 k(1− λ )+2kλv 2 1 )(4ρ − 2kλv 2 1 )+2kλv 2 1 (v 1 (1+k(1− λ ))+2kλv 2 1 ))> 0 Again, we use the fact that 4ρ − 2kλv 2 1 > 0 in the interior solution region. Proof of Corollary 2 Let us simplify and rewrite i i : i i = ρ (v 1 (1− k(1− λ ))− 2kλv 2 1 )− kλv 3 1 4ρc +2kλv 2 1 (ρ − c) The partial derivative with respect to λ : ∂i i ∂λ = (ρv 1 k− 2kρv 2 1 − kv 3 1 )(4ρc +2kλv 2 1 (ρ − c))− 2kv 2 1 (ρ − c)(ρ (v 1 (1− k(1− λ ))− 2kλv 2 1 )− kλv 3 1 ) (4ρc +2kλv 2 1 (ρ − c)) 2 The denominator is always positive, so let us focus on the numerator: 4ρc (ρv 1 k− 2kρv 2 1 − kv 3 1 )+2kλv 2 1 (ρ − c)(ρv 1 k− 2kρv 2 1 − kv 3 1 )− − 2kv 2 1 (ρ − c)(ρv 1 kλ − 2kρλv 2 1 − kλv 3 1 )− 2kv 2 1 (ρ − c)ρv 1 (1− k) = = 4ρc (ρv 1 k− 2kρv 2 1 − kv 3 1 )− 2kv 2 1 (ρ − c)ρv 1 (1− k) = = 2ρkv 1 (2cρ − 4ρcv 1 − ((1− k)ρ +(1+k)c)v 2 1 ) 55 Weobtainthethird-degreeequationinv 1 thathasrootzero. 2ρkv 1 ispositiveinthepositive region, so the whole expression has the same signs as the quadratic equation in this region. Let us find the roots of the quadratic equation: D = 16ρ 2 c 2 +8ρc ((1− k)ρ +(1+k)c)> 0 The roots have the following form: v 1 1 = − 4ρc − p 16ρ 2 c 2 +8ρc ((1− k)ρ +(1+k)c) 2((1− k)ρ +(1+k)c) < 0 v 1 1 ≡ ¯v 1 = − 4ρc + p 16ρ 2 c 2 +8ρc ((1− k)ρ +(1+k)c) 2((1− k)ρ +(1+k)c) > 0 The parabola open downward, so it is positive for v 1 ∈ (v 1 1 ,¯v). And it is negative for v 1 > ¯v 1 (we are not interested in the negative region). Proof of Corollary 3 a. We prove it in a similar manner to Corollary 1. Firstly, we show that the effort is higher under the competitive case: e ∗ c − e ∗ m = v 1 (1+k) 4ρ − v 1 4ρ = kv 1 4ρ > 0 We omit the upper limit on the effort because it does not change the ordering. Next, we show that the boundary condition effort is higher in the star effect case: e b − e ∗ m = v 1 (1+k(1− λ ))+2kλv 2 1 4ρ − 2kλv 2 1 − v 1 4ρ = = (v 1 (1+k(1− λ ))+2kλv 2 1 )4ρ − v 1 (4ρ − 2kλv 2 1 ) 4ρ (4ρ − 2kλv 2 1 ) = = 4ρ (v 1 (1− kλ ))+2kλv 2 1 )+2kλv 3 1 4ρ (4ρ − 2kλv 2 1 ) > 0 56 It is always positive 4ρ − 2kλv 2 1 > 0 for the interior solution region. Finally, we show that the interior solution is higher than the monopoly one: e i − e ∗ m = (v 1 (1+k(1− λ ))+2kλv 2 1 )(4c+2kλv 2 1 )+2kλv 2 1 (v 1 (1− k(1− λ ))− 2kλv 2 1 ) (4ρ − 2kλv 2 1 )(4c+2kλv 2 1 )+(2kλv 2 1 ) 2 − v 1 4ρ The combined fraction is too big, so we study it by parts. The denominator has the following form: 4ρ ((4ρ − 2kλv 2 1 )(4c+2kλv 2 1 )+(2kλv 2 1 ) 2 )> 0 Let us simplify the numerator: 4ρv 1 (4c+2kλv 2 1 )+4ρ ((v 1 k(1− λ )+2kλv 2 1 )(4c+2kλv 2 1 )+2kλv 2 1 (v 1 (1− k(1− λ ))− 2kλv 2 1 ))− − v 1 4ρ (4c+2kλv 2 1 )+v 1 (2kλv 2 1 (4c+2kλv 2 1 )− (2kλv 2 1 ) 2 ) = = 4ρ ((v 1 k(1− λ )+2kλv 2 1 )(4c+2kλv 2 1 )+2kλv 2 1 (v 1 (1− k(1− λ ))− 2kλv 2 1 ))+ +v 1 (2kλv 2 1 (4c+2kλv 2 1 )− (2kλv 2 1 ) 2 ) = = 4ρ (4c(v 1 k(1− λ )+2kλv 2 1 )+2kλv 3 1 )+8ckλv 3 1 > 0 Both numerator and denominator are positive, so the whole fraction is also positive. b. Let us simplify and rewrite e i : e i = kλv 3 1 +c(v 1 (1+k(1− λ ))+2kλv 2 1 ) 4ρc +2kλv 2 1 (ρ − c) The partial derivative with respect to λ : ∂e i ∂λ = (kv 3 1 − cv 1 k+2ckv 2 1 )(4ρc +2kλv 2 1 (ρ − c))− 2kv 2 1 (ρ − c)(kλv 3 1 +c(v 1 (1+k(1− λ ))+2kλv 2 1 )) (4ρc +2kλv 2 1 (ρ − c)) 2 57 The denominator is always positive, so let us focus on the numerator: 4ρc (kv 3 1 − cv 1 k+2ckv 2 1 )+2kλv 2 1 (ρ − c)(kv 3 1 − cv 1 k+2ckv 2 1 )− − 2kv 2 1 (ρ − c)(kλv 3 1 − cv 1 kλ +2ckλv 2 1 ))− 2kv 2 1 (ρ − c)(cv 1 (1+k)) = = 4ρc (kv 3 1 − cv 1 k+2ckv 2 1 )− 2kv 2 1 (ρ − c)(cv 1 (1+k)) = = 2ckv 1 (((1− k)ρ +(1+k)c)v 2 1 +4ρcv 1 − 2cρ ) We obtain the third-degree equation in v 1 that has root zero. 2ckv 1 is positive in the positive region, so the whole expression has the same signs as the quadratic equation in this region. Let us find the roots of the quadratic equation: D = 16ρ 2 c 2 +8ρc ((1− k)ρ +(1+k)c)> 0 The roots have the following form: v 1 1 = − 4ρc − p 16ρ 2 c 2 +8ρc ((1− k)ρ +(1+k)c) 2((1− k)ρ +(1+k)c) < 0 v 1 1 ≡ ¯v 1 = − 4ρc + p 16ρ 2 c 2 +8ρc ((1− k)ρ +(1+k)c) 2((1− k)ρ +(1+k)c) > 0 The parabola open upward, so it is negative for v 1 ∈ (v 1 1 ,¯v). And it is positive for v 1 > ¯v 1 (we are not interested in the negative region). 58 Appendix to Chapter 2 Proof of Proposition 1 Let us exclude strategies that are dominated by other strategies: • 4 is dominated by 2: 1− g > 1− m> 1− m− c τ − c a . • 1− g− 1− m 1− m+g = 1− m+g− g(1− m+g)− (1− m) 1− m+g = m− g 1− m+g > 0 • 6 is dominated by 2: 1− g > 1− m 1− m+g > 1− m 1− m+g − c τ − c a • 8 is dominated by 2: 1− g+m> 1⇒ 1− g > 1− g 1− g+m > 1− g 1− g+m − c τ − c a • 10 is dominated by 2: 1− g > 1− g− c τ • 7 is dominated by 1: 0.5g > 0.5g− c τ − c a • 9 is dominated by 1: 0.5g > 0.5g− c τ The customer does not observe the firm’s actions, so the firms can deviate in 3: a n = 0 because it will increase the probability of buying for the non-matching type. The firm’s profit upon deviation is: m(0.5m+0.5(1− g)) = 0.5m(1+m− g). m > g by assumption; therefore, the has higher profit upon this deviation and 3 cannot be an equilibrium. Now, let us show that the firm has no incentives to price deviate. The customer beliefs in each scenario will be the same as before. If the firm deviates by increasing price, she losses some demand (either the match type or the non-match type), but the increase in price does cover this loss and the cost stays the same, therefore, the profit decreases. If the firm deviates by decreasing the price, she keeps the same demand and the same cost, but the price is lower; therefore, the profit decreases. As a result, the firm does not want to decrease or increase the price. 59 As a result, we are left with only 3 strategies: 1, 2, and 5. Let us first show the firm’s strategy choice under different m and g. Then, we check conditions for the firm to deviate in 5. We compare the payoffs in these three strategies. • 1 vs 2: 0.5g vs 1− g⇒ when g∈ (0.5,2/3), the firm chooses 2; when g∈ [2/3,1], the firm chooses 1. • 1 vs 5: 0.5g vs 0.5m− c τ − c a ⇒ when m− g≥ 2(c τ +c a ), the firm chooses 5; when m− g < 2(c τ +c a ), the firm chooses 1. • 2 vs 5: 1− g vs 0.5m− c τ − c a ⇒ when 2g+m≥ 2(1+c τ +c a ), the firm chooses 5; when 2g+m< 2(1+c τ +c a ), the firm chooses 1. If we combine the conditions, we would get the boundary depict on Figure 2.1. The decision depends on the costs of investment and the improvement in the message. Let us note that if c τ +c a > 1/6, the firm would never use the targeting technology. Let us look at the tip of the triangle: m− 2/3 =2(c τ +c a ). The left part is not bigger than 1/3, so if the right part is bigger than 1/3, the triangle does not exist. We have not checked the condition for deviation in 5. The customer does not observe the firm’s action, so she can potentially deviate to other signal distributions. The best deviation for the firm is to ( a m = 0,a n = 0) because (a m = 1,a n = 1) and (a m = 0,a n = 1) incur the same costs and have lower demands than (a m = 1,a n = 0). (a m = 0,a n = 0) decreases demand, but also reduces the costs. The firm’s profit upon deviation to ( a m = 0,a n = 0): m m+1− g [0.5g+0.5(1− g)] = 0.5m m+1− g . We need to compare profits under no deviation and deviation: 0.5m− c τ − c a vs 0.5m m+1− g − c τ ⇒ 0.5m m− g 1+m− g vs c a . Let us find how this boundary behaves in m− g axis. To do this, we make the doubled left part equal to a constant and solve for m: m m− g 1+m− g = b⇒ m 2 − (g +b)m− b(1− g) = 0. This is two hyperbolas, and the no-deviation region lies at the exterior part of them. We can solve this equation and get two roots: m 1,2 = g+b± p (g− b) 2 +4b 2 . The lower hyperbola is lower 60 than 0 for g < 1: m 2 increases in g and m 2 (1) = 0. ∂m 2 ∂g = 0.5− 0.5· 2· (g− b) 2 p (g− b) 2 +4b > 0. The higher hyperbola always increases: ∂m 1 ∂g = 0.5+ 0.5· 2· (g− b) 2 p (g− b) 2 +4b > 0; therefore, it is a convex function. As a result, it will intersect with the triangle first at the tipping point or at the triangle furthest right point. We want to know when the targeting equilibria exist. First, we show for which cost parameters the full triangle exist. Then, we find when it exists at all. We use c = c τ +c a to simplify the next derivations. Let us compute the function value at the tipping point (2/3,2/3 + 2c): (2/3 + 2c) 2c 2c+1 . The value at the most right point of the triangle is: 2c 2c+1 . We see that for c< 1/6, the tipping point has lower value of the function. It means that the function first crosses the tipping point and only then after some increase in c it crosses the rightest point. Therefore, to find the parameters when the whole triangle exists, we need to find when the firm does not deviate at the tipping point. The firm does not deviate when (2/3+2c) 2c 2c+1 ≥ 2c a ⇒c a ≤ (2/3+2c τ )c τ 1/3− 2c τ . 61 Figure A.3: Existence of the targeting equilibrium for different costs. Next, we find when there are no targeting equilibria. The m m− g 1+m− g =b moves to the upper left direction; therefore, it will cross the most right point last. We need to compute when the firm starts to deviate at this point to find the boundary. 1− 2c 3− 2c < 2c a ⇒ c a > 2− c τ + p (c τ − 2) 2 +2c τ − 1 2 . We plot these regions in c τ − c a axes in Figure A.3. 62 Proof of Proposition 2 Let us exclude strategies that are dominated by other strategies: • 3 is dominated by 1: 0.5g > 0.5m> 0.5m− c τ − c a . • 5 is dominated by 1: 0.5g > 0.5m> 0.5m− c τ − c a . • 7 is dominated by 1: 0.5g > 0.5g− c τ − c a . • 9 is dominated by 1: 0.5g > 0.5m> 0.5m− c τ . • 10 is dominated by 2: 1− g > 1− g− c τ 4, 6, 8 are not equilibrium strategies because the firm wants to deviate to ( a m = 0,a n = 0). It serves the whole market in each case, but (a m = 0,a n = 0) has lower costs. If the firm deviates,shehasthesamerevenue,butlowercosts,sotheprofitishigherunderthedeviation. Therefore, we are left with two undominated strategies: 1 and 2. When g ∈ (0.5,2/3), the firm chooses 2; when g∈ [2/3,1], the firm chooses 1. The firm does not price deviate by the same logic as in the proof of Proposition 1. Proof of Proposition 3 We showed that 3, 5, 7, 9, and 10 are dominated in the previous proposition proof, and it holds here as well. However, 4, 6, 8 are now not dominated by 10 because c a = 0 and the firm has the same payoff when it deviates to ( a m = 0,a n = 0). We are look- ing for the firm’s preferred equilibria, so let us show that the firm prefers 4 over 6 and 8. 1− m+g > 1⇒ 1− m > 1− m 1− m+g , so 4 provides a higher payoff. 1 − m− 1− g 1− g+m = 1− g+m− m(1− g+m)− (1− g) 1− g+m = g− m 1− g+m > 0,so4hashigherprofitthan8. There- fore, we are left with 3 strategies: 1, 2 and 4. Let us find when the firm chooses one over the others: 63 • 1 vs 2: 0.5g vs 1− g⇒ when g∈ (0.5,2/3), the firm chooses 2; when g∈ [2/3,1], the firm chooses 1. • 1 vs 4: 0.5g vs 1− m− c τ − c a ⇒ when g+2m≤ 2(1− c τ − c a ), the firm chooses 4; when g+2m> 2(1− c τ − c a ), the firm chooses 1. • 2 vs 4: 1− g vs 1− m− c τ − c a ⇒ when c τ +c a ≤ g− m, the firm chooses 4; when c τ +c a >g− m, the firm chooses 1. The firm does not price deviate by the same logic as in the proof of Proposition 1. 64
Abstract (if available)
Abstract
This dissertation includes two chapters with a focus on digital platforms topics. The objective of the first chapter is to understand the phenomenon of the investment into content creators by the platforms in the context of digital platforms. I consider platforms like YouTube, Twitch, and TikTok where some users earn money by creating content consumed by other users. These platforms can recommend content creators inside the platform on various pages. These recommendations help content creators to grow their audiences and effectively serve as investments into them. The content creators generate some revenue on the platform (e.g., paid subscriptions, advertisements). The platform and the content creator then split this revenue. This chapter tries to understand how competition between the platforms for content creators affect the equilibrium investment into content creators, revenue split and profits. I find that the platform has incentives to invest less into content creators compared to the monopoly case when there is some competition between the platforms. Moreover, the platform does not invest into big streamers if there is a star effect in the market. The welfare implications mainly depend on the model parameters. There only two relationships that always hold: the platform prefers the monopoly over the competition and the content creator prefers competitive regime over the monopoly. However, the star effect might the most preferred (the second best) or the least preferred option for the content creators (platform) depending on the parameters.
The second chapters studies how targeting affects consumer's willingness to pay and equilibrium pricing decisions. I consider a situation where a firm uses internet advertising to make customers aware about its product. The customer seeks for a product that is good fit for him. The firm has initial message about its product based on truthful claims about the product. However, the claims cannot convey all the information that the customer needs to understand whether the product is a good fit for him. Therefore, the message is characterized by its precision -- how likely the customer infers that the real good fit product is good fit for him. The firm can purchase a targeting technology that helps to analyze the customer's preferences to create a new signal. The new signal might have higher or lower precision than the original signal. There are four equilibria emerge. If the precision of the original is not too high, the firm does not purchase the targeting technology, serves the whole market and sets a relatively low price. If the precision of the original is sufficiently high, the firm does not purchase the targeting technology, serves the customers who think that the product is a good match for them and sets a relatively high price. If the new signal has higher precision and the cost to increase in precision ration is relatively low, the firm purchases the targeting technology, serves the customers who think that the product is a good match for them and sets a relatively high price. Finally, when the new signal is vaguer than the original one and the costs of the new message are really low, the firm purchases the targeting technology, serves the whole market and sets a relatively low price. I find that the price might be non-monotonic in the precision of the initial message.
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University of Southern California Dissertations and Theses
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Asset Metadata
Creator
Lukibanov, Ilya
(author)
Core Title
Essays on digital platforms
School
Marshall School of Business
Degree
Doctor of Philosophy
Degree Program
Business Administration
Degree Conferral Date
2022-08
Publication Date
05/27/2022
Defense Date
03/07/2022
Publisher
University of Southern California
(original),
University of Southern California. Libraries
(digital)
Tag
content creators,digital platforms,OAI-PMH Harvest,privacy,talent management
Format
application/pdf
(imt)
Language
English
Contributor
Electronically uploaded by the author
(provenance)
Advisor
Mayzlin, Dina (
committee chair
), Camara, Odilon (
committee member
), Dukes, Anthony (
committee member
)
Creator Email
ilukibanov@nes.ru,ilya.lukibanov.phd@marshall.usc.edu
Permanent Link (DOI)
https://doi.org/10.25549/usctheses-oUC111339145
Unique identifier
UC111339145
Document Type
Dissertation
Format
application/pdf (imt)
Rights
Lukibanov, Ilya
Internet Media Type
application/pdf
Type
texts
Source
20220608-usctheses-batch-945
(batch),
University of Southern California
(contributing entity),
University of Southern California Dissertations and Theses
(collection)
Access Conditions
The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the author, as the original true and official version of the work, but does not grant the reader permission to use the work if the desired use is covered by copyright. It is the author, as rights holder, who must provide use permission if such use is covered by copyright. The original signature page accompanying the original submission of the work to the USC Libraries is retained by the USC Libraries and a copy of it may be obtained by authorized requesters contacting the repository e-mail address given.
Repository Name
University of Southern California Digital Library
Repository Location
USC Digital Library, University of Southern California, University Park Campus MC 2810, 3434 South Grand Avenue, 2nd Floor, Los Angeles, California 90089-2810, USA
Repository Email
cisadmin@lib.usc.edu
Tags
content creators
digital platforms
talent management