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Three essays on agent’s strategic behavior on online trading market
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Three essays on agent’s strategic behavior on online trading market
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THREE ESSAYS ON AGENT’S STRATEGIC BEHAVIOR ON ONLINE TRADING MARKET by Haojun Yu A Dissertation Presented to the FACULTY OF THE USC GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (ECONOMICS) August 2015 Copyright 2015 Haojun Yu Dedication To my family, for endless support. ii Acknowledgments When I get to the part of writing acknowledgments, I feel both happy and sad. It means my thesis and my study here at USC economics is close to an end. I look forward to moving on to my next stage of life, while feel sorry to have to leave. Before I leave, I would like to thank many people. Without their help, this thesis would be almost impossible. First and foremost, I would like to express my greatest gratitude to Professor Guofu Tan, my main supervisor and the chair of the dissertation committee. Professor Tan has spent countless hours discussing with me from research ideas, model details, to writing and pack- aging papers. He is always encouraging on my exploring my research interest and never sets boundaries. I began my study in theoretical IO, but almost totally switched to empirical work in my later years. Professor Tan is tolerant to my choices and being very supportive, although he has to put in even more effort to supervising me on my empirical work. In traditional Chi- nese culture, teachers are respected as fatherhood. I always respect Professor Tan as my role model to learn from in doing research and in being academic professionals. I am also very grateful to other committee members. I especially thank Professor Geert Ridder for discussing econometrics issues in my work. I should have asked a lot of stupid questions and made countless mistakes in the process of learning and applying structural esti- mation tools, and Professor Ridder is very patient and repeatedly answered all my questions. I also benefited a lot from econometrics group study organized by Professor Ridder. Also, I thank Professor Simon Wilkie for discussing my papers and inspiring me with different thoughts. Professor Wilkie was out of town in my last two years at USC, yet every time he iii came back to USC, he always spent some time to hear my work progress and give advice. Professor Anthony Dukes from Marshall also provided substantial guidance to my theory work. I also thank other USC faculty members, including but not limited to Yuwei Hsieh, Juan Carrillo, John Strauss, Cheng Hsiao, Harrison Cheng, Roger Moon, Jeffrey Nugent for encouragement and advice. I also indebted to the financial support provided by USC, enabling me to focus on my research without worrying about basic needs. I also thank my classmates and friends at USC. Specially I am grateful to Cheng Chou, for giving me a lot of professional advice on econometrics. And to Jin Wang, for growing up together as USC. I hope we can coauthor some papers together. Also I thank my coauthor Lin Liu for working together on mutual interests. And to Xing Zhang at USC and Menghan Xu at UCLA for doing papers together currently. There are too many professors and friends I would like to say thank you. Sorry for not listing all the names here. It is too long a list. Last, I want to express my greatest thanks to my family, who provided me endless support in my study and in my life. iv Contents Dedication ii Acknowledgments iii List of Tables vii List of Figures ix 1 Introduction 2 2 Measuring Effectiveness of Feedback and Authorization on a Platform 5 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2 Background and data description . . . . . . . . . . . . . . . . . . . . . . . . 9 2.3 Empirical model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.4 Model findings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 3 Seller’s Management of Rating Scores through Dynamic Pricing 25 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 3.2 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 3.3 Background and Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3.4 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 3.5 Structural Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 3.6 Model Extension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 3.7 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 4 Display Order and Consumer Search of Asymmetric Products (joint with Lin Liu) 70 4.1 introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 4.2 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 4.2.1 Benchmark: Zero Search Costs . . . . . . . . . . . . . . . . . . . . 79 4.2.2 Descending Display Order . . . . . . . . . . . . . . . . . . . . . . . 81 4.2.3 Ascending Display Order . . . . . . . . . . . . . . . . . . . . . . . . 84 v 4.2.4 Display Order Selection . . . . . . . . . . . . . . . . . . . . . . . . 86 4.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 Reference List 101 A Appendix 1 106 vi List of Tables 2.1 Summary statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.2 Tmall seller . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.3 Ratings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.4 Effect of Quality Signals on Sales . . . . . . . . . . . . . . . . . . . . . . . 19 2.5 Effect of Ratings on Sales: fixed effect . . . . . . . . . . . . . . . . . . . . 20 2.6 Effect of Quality Signals on Sales: IV . . . . . . . . . . . . . . . . . . . . 21 2.7 Effect of Quality Signals on Sales: FE and IV . . . . . . . . . . . . . . . . 21 2.8 Effect of Prices on Other Markets on Prices: first step in IV . . . . . . . . . 22 2.9 Effect of Prices on Other Markets on Prices: first step in FEIV . . . . . . . . 22 2.10 Effect of Quality Signals on Sales Probability . . . . . . . . . . . . . . . . 23 2.11 Effect of Quality Signals on Sales Probability: FE . . . . . . . . . . . . . . 24 3.1 Data Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 3.2 Distribution of Rating Scores . . . . . . . . . . . . . . . . . . . . . . . . . 36 3.3 Transition of Rating Scores . . . . . . . . . . . . . . . . . . . . . . . . . . 36 3.4 Correlation of Rating Scores and Sales . . . . . . . . . . . . . . . . . . . . 38 3.5 Transition Probability Estimates . . . . . . . . . . . . . . . . . . . . . . . . 53 3.6 Demand Estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 3.7 Model Fits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 3.8 The Effect of Number of Sellers on Pricing . . . . . . . . . . . . . . . . . . 62 vii 3.9 Asymptotic Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 A.1 Effect of Ratings on market share . . . . . . . . . . . . . . . . . . . . . . . 107 A.2 Effect of Ratings on market share: fixed effect . . . . . . . . . . . . . . . . 108 A.3 Effect of Ratings on market share: IV . . . . . . . . . . . . . . . . . . . . . 109 A.4 Effect of Ratings on market share: FEIV . . . . . . . . . . . . . . . . . . . 110 viii List of Figures 3.1 Rating Score Distribution over Time . . . . . . . . . . . . . . . . . . . . . . 37 3.2 Prices Age Relationship . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 3.3 Sales Age Relationship . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 3.4 Seller’s Inequality in Sales . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 3.5 Pricing-Rating Relationship . . . . . . . . . . . . . . . . . . . . . . . . . . 45 3.6 Pricing-Rating Relationship: comparative statics . . . . . . . . . . . . . . . 46 3.7 Pricing-Rating Relationship: comparative statics . . . . . . . . . . . . . . . 46 3.8 Prices Fitness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 3.9 Prices Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 3.10 Prices Comparison for two types . . . . . . . . . . . . . . . . . . . . . . . . 68 4.1 a snapshot of search results of laptops on Alibaba’s Taobao Mall . . . . . . . 91 4.2 Illumination of the total profit of the two sellers - search cost relationship . . 92 ix 1 Chapter 1 Introduction Online trading market plays a more and more important role in today’s economic activities. Its success in business is not possible with the design of trading platforms. As an attempt to boost transaction, platforms like Amazon or eBay in US, Alibaba in China, etc. designed tools to reveal seller’s reliability, facilitate communication between sellers and buyers, delib- erate the display of products, etc. This thesis looks at some of the online trading platform’s design and its implication on buyer and seller’s choice as well as the platform’s profit. The analysis contains both theoretical and empirical work. The first chapter looks at the design of platform’s quality signaling, often referred to as the reputation system. I look at Alibaba’s platform where both centralized and decentralized quality signals are used. In the chapter, I empirically examine how consumers interpret the quality signals and make purchasing decisions based on beliefs of product quality. Specif- ically, I examine whether different quality signals work as substitute or compliments. The demand is estimated both in the game-theoretic framework and non-game-theoretic frame- work. The second chapter looks at the platform’s design of reputation system on participating seller’s pricing strategy. From previous chapter and earlier literature, we know buyers are more likely to buy from high rating scores sellers, but sellers’ behavior to affect rating scores is less clear. In this paper, I take advantage of Alibaba’s unique design of rating scores system for identification. The design awards sellers both on quality and sales: given quality or probability of receiving good ratings, the more the sellers sale, the faster they can accumulate rating scores. Based on this observation, I build a single agent dynamic pricing model to capture the sellers’ incentive to manage rating scores. The seller’s pricing affect both current 2 period profit and rating scores in the future. As a result, sellers are willing to undercut prices for rating scores dynamic concerns. Besides, for estimation, sellers are assumed to have two types of service quality. The mixed type model is estimated by nested fixed point algorithm. I confirm that demand is shifted to sellers with high rating scores and having more sales can accelerate rating score accumulation, implying sellers have incentive to manage rating scores. From counter factual analysis, the prices will be 0.1-1% higher if the sellers do not care rating score dynamics. The findings confirm the effectiveness of Alibaba’s design of its rating score system. The third chapter looks at the platform’s arrangement to display products of asymmetric fitness. This is a coauthered paper with Lin Liu. We are interested in how the display order will affect consumer’s choice, participating seller’s competition and the platform’s profits. Being placed on top will give the product some advantage of being chosen. Specifically, we found it is not always beneficial to display high fitted product first, due to the competitive effect. As products are potentially of different fitness, such advantage is different. Since high fitted product can always get the demand who finds the low fitted product not fit, it will value the advantage of being on top less. In contrast, the low fitted product will value the top place more. If the low fitted product is placed on bottom, it will set very low prices to compete for demand, strengthening the pricing competition on the platform. In this case, the platform’s profit, as a cut of the total profits of all the participating sellers, will be harmed. As a result, the platform will optimally choose to place the low fitted products on top, even doing so will harm the consumers and the high fitted product. Though the empirical analysis in the first and second chapter of the thesis is carried out using data from one particular platform, the Alibaba’s platform, the theoretical reasoning is applicable to other online trading markets as well. Platforms may have particular design of its own, but the reaction of sellers and buyers as rational economic agents reflects general economic insights. The work should have external validity in this sense. 3 Last, I aim to frame each chapter as an independent, self-contained paper. So forgive me for being verbose to repeat some background or concept across chapters. 4 Chapter 2 Measuring Effectiveness of Feedback and Authorization on a Platform abstract The paper checks the effectiveness of two measures of quality signals, the feedback and authorization, on consumer’s consideration set and transaction occurrence on online trading platforms. Taking Taobao.com as an example, the paper estimates the buyer’s valuation of sellers’ scores from feedback and whether sellers are authorized as Tmall sellers. The esti- mates find both measures are effective and the two measures are substitutes. The sign of the effect does not change whether the empirical model is modeled as game-theoretical or not. And the results are robust with or without using instruments for prices in the estimation. The finding confirms the effectiveness of both quality signals. The separation will emphasize the effect of authorization, but the effect from feedback scores is weakened. 2.1 Introduction With the prevalence of Internet access, e-commerce has witnessed a fast growth in the last decade in China. One important aspect of this trend is the development of online shopping. Among many shopping sites, Taobao is now the leading retail trade platform, with 500 mil- lion registered users and 60 million daily visits in 2012. Like any other trade platforms such as Amazon or eBay, quality signaling is one important element in constructing the plat- form. Taobao provides both decentralized and centralized mechanism to reveal information 5 of the quality of sellers’ products or services. For the decentralized quality signaling, Taobao provides a feedback rating system. Buyers are asked to give rates and reviews on their past purchasing experience, about quality of the product, shipping speed, and services in the trans- action. These rates are aggregated into a score for the sellers and displayed on the sellers’ introduction page. From 2008, Taobao also provides a centralized quality control. It autho- rizes some sellers as "Tmall sellers" if the sellers satisfy certain basic screening conditions and agree to deposit certain amount of money in a saving account to be used exclusively for compensating customers when misbehavior in the transaction happens. The sellers also need to agree on a stricter damage compensation standard and pay for the title. In June 2011, Alibaba group, the owner of Taobao, decides to separate the operation of ordinary sellers and Tmall sellers and lists Tmall sellers separately on a different website, namely Tmall.com. Consumers can go to the new website if they prefer only Tmall sellers. However, if they search products on taobao.com, at least some Tmall sellers are still displayed in the search- ing results on Taobao. Meanwhile, the charging for Tmall users increases dramatically. As a consequence, Tmall users complained and threatened to leave the platform. Though Alibaba finally agreed to postpone the increase of charging fee, it still insisted that the separation into two platforms can benefit both sellers and buyers as the new operation takes care of buyers’ desire for good quality better and better discriminate sellers. Besides, in January 2012, to further promote Tmall platform, Alibaba changes the Chinese name of Tmall from "taobao shangcheng" to "tianmao" (sky-cat,the Chinese homophobic of Tmall) to make it sound less similar to Taobao, as a way to give consumers an impression of two distinct platforms. The paper aims to empirically assess such business practice. The purpose of this paper is to estimate buyers’ valuation of the centralized and decentralized quality signaling and to predict the welfare implication of the separation of Taobao and Tmall. The effectiveness of the feedback (the decentralized quality signal) and the Tmall authorization (the central- ized quality signal) depends on how buyers interpret these signals and translate them into a measure on quality, and further into their purchasing behavior. One empirical question is 6 how informative is the feedback and authorization from the perspective of buyers and how the two measures substitute each other. If feedback system is sufficiently informative and authorization does not add more information to buyers’ inference on sellers’ quality, then the separation of two platforms does not benefit the platform users much; on the other hand, if feedback is not informative, or authorization provides more information besides feedback, then the separation of two platforms can benefit the platform users. To answer these questions, I need to estimate the demand of sellers, and examine how quality signals shifts demand. The demand is measured in both the sales in equilibrium as well as whether the sellers are very considered by the buyers, i.e. the consideration set, as proxied by whether the sellers have realized positive sales.I try two different settings for how total sales is determined. In one setting, I use the standard multinomial logit model. Buyers are assumed to make discrete choice to pick one seller, so the choice probability can be aggregated and reflected by market share. (Berry, Levinsohn, and Pakes 1995, hereafter referred to as BLP) The model can used to estimate the demand side of oligopoly competition, with or without the supply side optimization (Nevo, 2000b). It has been used widely in estimation of brand competition, market power, merger (Nevo, 2000a) and introduction of new products (Petrin, 2001). It is also used to estimate the demand side of a two-sided market, like newspapers (Fan, 2013), yellow page (Rysman, 2004). In the setting, sellers are competitive and game-theoretically thinking: when they make pricing decisions, they would consider the price reaction of the other sellers. On the other side, given the large number of sellers on the websites, the sellers might not consider other competitor’s prices in a game- theoretically way. So in another setting, I assume the total sales is affected by the seller’s own price and market conditions. When sellers make pricing decision, they are not game- theoretically thinking: they take the market conditions as given, and only consider the own price elasticity. In that case, a linear demand model is used. 7 In this chapter, I use both the linear demand model and the standard multinomial logit model to estimate the total sales. Also, I use linear probability model to estimate the proba- bility of sellers realizing positive sales. I look at the sales of digital single lens reflex (DSLR) cameras on Taobao from September 2011 to May 2013. The data are collected by a Python web-scrapping program. The data collection process is described in the appendix. The data set contains more than 300 camera kinds and more than 15,000 sellers. The estimates of a standard multinomial logit model reveals both being Tmall sellers and accumulating high rate scores have a positive effect on market share, indicating both the cen- tralized and decentralized quality signaling are effective. The two measures are substitutes, as the interaction term of scores and being Tmall sellers are negative. The estimation of the linear demand reveals the same pattern. In the estimation, the prices of the products are endogenous, as unobserved quality affects both the buyer’s choices and the seller’s pricing. To control the endogenous issue of prices, the model is estimated using the camera-store fixed effect. Besides, I also used lagged prices as instruments for current period prices. Another instrument used is the difference of prices to average prices of other cameras sold by the same sellers. The instrument variable estimator change the magnitude but the signs remains, reflecting the robustness of the estimator. This paper is a case study of two-sided market. The basic idea of pricing in two-sided market is first proposed in the seminal works of Caillaud and Jullien (2003), Rochet and Tirole (2003), Rochet and Tirole (2006) and Armstrong (2006), among others. In these early papers, the effect of users on each side is homogeneous and the transaction between the two sides is not explicitly specified. Weyl (2010) extends the platform pricing model to allow the effect of users be heterogeneous and compare the efficiency loss of monopoly platform as compared to the benchmark of social optimal. Most of the papers focus on pricing of the platform without specifying the transaction of users on the two sides. They do not deal with questions such as how the interaction of users on different sides depends on platform’s pricing, or how platform’s pricing affects the price a side user (seller) offer to the other side 8 (buyer). This paper complements the two-sided market literature by explicitly specifying the transaction process and how it is affected by platforms’ pricing and other measures. The paper reveals a positive role of quality control, both centralized and decentralized, indicating the building of a platform is much more than merely setting prices and letting users on the two-sides get interacted automatically. The design of platform is an interesting direction in later research. (see Hagiu, 2009) There is also many papers discussing the evaluation of reputation on trading platforms like eBay. See Bajari and Hortacsu (2003) and Dellarocas (2006) for a survey of the effect of feed- back on eBay. In the works of Resnick and Zeckhauser (2002), Houser et al. (2006), Resnick et al. (2006), and many others, they find positive correlation between the price of an item and the feedback that a seller has received on eBay. Most of the works use cross-sectional data, except Cabral and Hortacsu (2010). Some papers do not discuss the endogeneity of feedback explicitly. Some works use experiment to guarantee exogeneity, for example in Resnick et al. (2006). The discussion of endogeneity focuses on the omitted variable bias, as intrinsic quality affect both market performance and rating scores received. The seller’s management of rating scores certainty adds more dimension of possible endogeneity, but is less discussed in these works. The exception is Cabral and Hortacsu (2010). 2.2 Background and data description I collect sales of digital single lens reflex (DSLR) cameras on Taobao on a monthly base from September 2011 to May 2013. I look at the market of DSLR cameras for the follow- ing reasons: first, camera is a durable goods and is usually sold one unit per buyer, which fits the assumption in the multinomial logit estimation model. For the same reason, buyers are less likely to be returned customers, eliminating the probability of buyers having more information about the sellers than econometrians by repeated purchases. Second, cameras are valuable goods such that buyers care its quality more as compared to small items like, 9 for example, UV filters. Third, camera kinds can be clearly defined as in search and display, and the measure on their quality is more homogeneous. That facilitates data collection and minimize the misconception of the buyer, seller and econometrician. For example, if some- one searches "Canon 500d" on Taobao, the results are more well-defined than searching, say, "Nike running shoes, red", and buyers and sellers are more likely to agree on the quality of cameras than Nike running shoes. The measure of the seller’s quality is more on the service provided in the transaction, rather than other factors such as the fitness of the shoes. The data set includes 324 kinds of cameras - lenses bundles, sold by more than 15,000 sellers. After grouping same cameras but different cameras - lenses bundles, the data include 160 different camera models. For each cameras - lenses bundle, I collect data on monthly sales, prices, shipping fee, and sellers’ characteristics. A description of the basic data statis- tics is listed in table 2.1. The rate scores are on a 1 to 5 basis. There are three measures: whether the sellers truthfully describe the products; whether the deliver is fast and satisfac- tory; and whether the overall service is good. Most sellers’ scores are near 5. The average score is as high as about 4.85. Not surprisingly, the scores on the three measures are pretty similar, resulting collinearity of the measures, so only the first measure is used in regression. About 2.7% of the sellers are Tmall sellers in the dataset. Remember only the sellers listed on Taobao.com’s search results are collected in the data set, so the selected Tmall seller may not be a representative sample. 48% of the sellers accept credit card in payment. Stores have an average of about three years of doing business on Taobao.com. The average amount of deposit for damage compensation is about 1200 yuan. The dispersion of deposit is uneven: some sellers have no deposits at all; for those with deposit, the amount is usually between 3000 and 8000 yuan. The average price for the camera - lenses bundle is around 8700 Yuan. Depending on different bundles, the range of prices is pretty large. The sales of cameras across sellers and across camera models are also very dispersed, known as the 80-20 rule on online trading: 20% of top sellers can achieve more than 80% of the sales. The bottom majority can sell less than two camera sets per month. 10 Table 2.1: Summary statistics Variable Mean Std. Dev. Min. Max. N Label rate_1 4.850 0.172 1 5 475403 scores on 1-5 base, measure 1 rate_2 4.863 0.17 1 5 354896 score on 1-5 base, measure 2 rate_3 4.873 0.165 1 5 475116 score on 1-5 base, measure 3 tmall 0.027 0.162 0 1 583894 tmall sellers prices 8715.401 9192.642 1500 58500 583894 prices sales 0.644 8.870 0 1505 583894 monthly sales shipfee 20.481 60.659 0 10000 583894 shipping fees credit_card 0.479 0.5 0 1 583894 whether credit card is accepted cam_num 22.602 24.865 1 321 583894 number of cameras sold prepay 1230.61 2954.884 0 127000 554767 Deposit of damage compensation store_dur 39.097 26.314 0 115 383382 # of months operating on Taobao Table 2.2 and table 2.3 looks at the relationship of market share and quality signals. Table 2.2 looks at the relationship of market share and being Tmall sellers. The chance of selling is significantly larger for Tmall sellers (13.2%) than non-Tmall sellers (8.2%) but the trans- action volume is smaller (3.7 v.s. 5.7 cameras). That indicates more sales inequality among non-Tmall sellers. The relationship of market share and feedback are u-shaped. The chance of selling and transaction volume is highest for sellers of rate scores 4.8 and 4.9, but not 5. The causality can be the other way: large transaction volume leads to more chance of being rated and more noisy rates, increasing the odds of getting bad score. In the estimation model, I add a square term of the rate in the estimation model to measure this non-linearity. In one other setting, I used dummies for rating scores category to measure the non-linearity. Table 2.2: Tmall seller tmall sales is positive average sales 0 .0820 5.738 1 .1322 3.720 Total .0833 5.654 11 Table 2.3: Ratings rate_1 sales is positive average sales 4.6 .04769 1.6374 4.7 .10674 10.338 4.8 .14291 9.4791 4.9 .1087 5.1741 5 .04263 1.8498 Total .09938 7.2373 The tables indicates the both the two measures of sellers’ quality has a positive effect on sales, measured by probability of positive sales or units sold conditional on positive sales. I try to control other factors shifting demand in the estimation model. 2.3 Empirical model In order to understand the efficiency of the feedback and authorization system and its impact on the profitability of the sellers and the platform, the first step is to evaluate buyers’ evalua- tion of these quality signals. To do that, I estimate the demand model. I discuss two different demand settings: one is linear demand model; the other is multinomial logit demand model. At each time period t, there are K t markets, defined by different camera-lenses combina- tions. On each market, there are N kt number of sellers. In the linear demand model, the sales for seller j on market k at time t is simply defined as a linear model: s jkt =b x jkt +g z kt +x jk +e jkt The x jkt contains the seller’s logged prices, quality signal and other control variables and the z kt contains variables to measure the market condition. x jk is the camera - seller fixed effect, and e jkt is the random error. e jkt is assumed to be independent and from the same distribution. I allow the fixed effect to be correlated with the independent variables. The 12 fixed effect contains unobserved quality of the sellers, which should be correlated with the quality signal and the prices. So the model is estimated by a fixed effect model. In the multinomial logit model, consumer i gets a utility u i jkt =b x jkt +x jkt +e i jkt from purchasing from seller j of market k at time t. x jkt contains the seller’s logged price, quality signal and other control variables. The variables to measure the market condition are not contained. If she does not purchase from any of the sellers, she get utility u i0kt =e i0kt from some outside option. Assuming thee’s follow a type II extreme value distribution, the probability of choosing seller j has a closed form solution as sh jkt = exp(b x jkt +x jkt ) 1+å j exp(b x jkt +x jkt ) Given large number of sellers, the probability can be understood as the market share of product j on market k at time t. With little adjustment, I can get the linear form of market share such that ln(sh jkt ) ln(sh 0kt )=b x jkt +x jkt In another setting, to estimate the effect of rating scores on consumer’s consideration set, I use linear probability model to estimate whether the sellers have positive sales. That is, 1(s jkt > 0)=b x jkt +g z kt +x jk +e jkt where 1(:) is the indicator function. I use linear probability model instead of logit or probit model, so the fixed effectx jk can be included without adding much computation. In my estimation model, the observed characteristics include whether sellers are Tmall authorized, sellers ratings, and other measures of services such as whether credit card is 13 accepted, whether payment after receiving the products is allowed, when the store is opened on Taobao, the amount of deposit for damage compensation payment, et al. The unobserved information includes expression of the webpage, literal reviews which is hard to quantita- tively measure, picture of the products, et al. All of them can be viewed as signals of the seller’s quality. I define the market as camera-lenses combination in a month, so there are about 280 to 300 markets per month. I define the market as one kind of cameras rather than all cameras in order to make the market share of each seller not too small. The model can fit the conjecture of how consumer makes choices: before searching on the website, she already knows which camera models she is looking for. By assuming market being independent, the substitutes of cameras are ruled out. The potential problem with the setting is that the sub-population for each market is different. For example, consumers for a more-advanced camera model is likely to be richer, and care quality signal more and prices less; while consumers for entry level cameras may care quality signal less and prices more. The estimation will only give the average effect. Second, for those sellers selling more than one kind of cameras, their decisions on prices, score accumulation, design of the website, is not independent for each camera. That dependence is omitted in the model. Both the total sales (by the linear demand model and the multinomial logit model) and the probability of positive sales are estimated with a camera - seller fixed effect. The fixed effect has controlled some time-invariant unobserved factors. To overcome other possible endogenous issue of prices, I also use instrument to control the problem. I have tried two different choices of instruments. One is the lagged prices p jkt1 . The other choice is to use the average prices deviation from the average, that is p jk 0 t ¯ p k 0 t k 0 6=k . The idea is: if a seller is efficient and he sets prices on average lower than his competitors on other cameras, he is likely to set lower prices for this camera as well. When the markets are independent, then the prices on other markets (k 0 6= k) can be used as instrument for the k market. The choice 14 of instruments may has its own drawback. Nevertheless, I find the results remained in the instrument variable estimation, indicating that the results are pretty robust. 2.4 Model findings All tables presenting the main estimation results are left at the end of this chapter. I discuss settings when rating scores are treated as continuous variables. More extra tables of different model specifications (rating scores treated as discrete variables) are left in the thesis appendix for further reference. Table 2.4 to table 2.7 list the regression results of OLS, fixed effect, instrument variables and IV-FE model. The dependent variables are total monthly sales. In all the 4 tables, the first column does not control the camera’s fixed effect, and column (2)-(4) control the camera’s fixed effect. In table 2.4 and table 2.5, column (5)-(8) lists the results for the subsample of those sellers who have realized positive sales. From the table, we find a strong negative price effect. 1% increase in prices decrease the sales by 1.2 units. The effect of rating scores is even stronger, especially at low levels. When rating scores are high, the effect is actually negative. That is consistent to the descriptive tables we saw earlier; yet the reason is not clear. Being Tmall sellers also increases sales, but the magnitude is pretty small. The prices effect and rating score effect are much larger for the sub-sample of those sellers with positive sales. For this sub-sample, 1% increase in prices decrease the sales by around 2.5 units. The effect of rating scores is also stronger. After controlling the camera-seller’s fixed effect, the effect of rating scores becomes not significant. The main reason is that the variation of rating scores are pretty small over time, as they are mainly a measure of overall long-term quality. The effect of prices is stronger after controlling the seller’s fixed effect. 1% increase in prices decrease the sales by 2.4 units for the full sample, and by more than 10 units for the sub-sample with positive sales. If good sellers are also more cost efficient so that they can afford to set lower prices, then the OLS 15 estimation will underestimate the effect of prices. The estimation results are consistent to that hypothesis. The prices in the regression are potentially endogenous, as the sellers will take the unob- served quality into account when setting the prices. To overcome the endogeneity of prices, the model is also estimated with instruments. The instruments used for regression in table 2.6 and 2.7 are the average prices deviation of other cameras sold by that seller. From the tables, the effects of prices and rating scores do not differ too much with the results without the instruments, indicating the endogeneity issue may not be so severe in this application. The first stage results for the instrument variable regression are listed in table 2.8 and 2.9. Again, the camera’s fixed effect is not controlled in the first column but controlled in the rest three columns. The effect of prices deviation from the average for different camera models is pretty strong and significant. And consistent with our hypothesis, sellers with higher ratings set prices lower rather than higher without controlling the seller’s fixed effect. After the seller’s fixed effect is controlled, the sellers with higher ratings set higher prices. In another measure of outcome, I consider the effect of quality signals on buyer’s consid- eration set indexed by whether the seller realized sales or not. Table 2.10 and 2.11 list the linear probability model of getting positive sales, without and with the seller’s fixed effect. 1% increase in price decrease the probability by 11.2 percentage point. And the effect of rating scores is positive except at almost the level of 5 stars. After controlling the fixed effect, the prices effect is even stronger: 1% increase in price decrease the probability by 15.6 per- centage point. But the effect of rating scores goes away. In both the setting, the interaction of rating scores and being Tmall sellers are negative and significant. It indicates the buyers care less of ratings on Tmall when they decide to consider the product or not. This is the only settings that the interaction term is significant. The regression results with logarithm of market share as dependent variables are listed in the appendix at the end of the thesis. The results are similar to the specification discussed here, though the magnitude and significance may differ in some settings. 16 2.5 Discussion There are other possible choices of demand setting, such as the nested logit model or the random coefficient logit model (blp model). Indeed, compared to the random coefficient multinomial logit model, the current model makes more strict assumptions on own elasticity and on cross elasticity. See BLP (1995) or Nevo(2000) for further discussion. These model settings are not used due to the data set structure. On the market, there are many small sellers, and the market share is very small for most of the sellers even under the current definition of market. In those case, estimating the nested logit or random coefficient multinomial logit model will have computational problems that make the convergence very hard 1 . In the further work, a possible extension is to use a subsample of relatively large sellers and carry the random coefficient multinomial logit model on the subsample. If I make assumption of perfect competition, at least among those with a good history of credit, then the estimation can be made easier. I can assume the choices of sellers are only due to independent random terms after controlling sellers’ characteristics. In this case, a Poission regression or even linear regression on sales can serve the purpose. For a more detailed discussion, see Burda et al. (2009) and Burda et al. (2012). Another issue not discussed is that I only considered the endogeneity of prices but not the endogeneity of the quality signal. Since the ratings are aggregated from previous buyers’ feedback, and the seller can choose to be the Tmall seller or not, so potentially the quality signal is also endogenous. In Wang Jin’s paper (Wang, 2015), the selection of being Tmall seller or not is considered in a more structural estimation method. The possible endogeneity of ratings is not discussed, and the prices are also assumed to be exogenous. In the next chapter, the endogeneity of ratings is explicitly considered. I examine another quality of signal, and the evolution of the signal is explicitly considered in the seller’s dynamic pricing behavior. See the next chapter for more details on the model and estimation. 1 See the paper by Gandhi et al., 2013 for more discussion 17 2.6 Conclusion The chapter examines the buyer’s evaluation of seller’s quality signals by estimating the demand model. The estimation results all points out that both signals are valued by the buyers, and the two signals are substitutes. The results are robust under different demand settings, and with and without using instruments. From the estimation finding, I predict the separation of the platform may not work as good as the Alibaba group claims. The separation of the platform will weaken the effect of the decentralized quality signal. However, due to the data limit, since I do not have information on all the sellers on Tmall.com, the separation may have some positive effects of attracting more sellers onto the platform, or better separating the buyers on their willingness to pay for better quality. These issues are left for future research. Tables 18 Table 2.4: Effect of Quality Signals on Sales sales sales sales sales sales sales sales sales lprices -0.265 -0.945 -1.281 -1.281 -1.227 -2.330 -2.474 -2.463 (0.017)*** (0.051)*** (0.069)*** (0.069)*** (0.197)*** (0.555)*** (0.718)*** (0.718)*** rate_1 5.269 6.066 2.757 2.767 73.036 75.061 38.344 38.691 (0.451)*** (0.451)*** (0.643)*** (0.643)*** (10.765)*** (10.679)*** (12.074)*** (12.075)*** rate1sq -0.727 -0.848 -0.407 -0.407 -9.336 -9.866 -5.590 -5.695 (0.053)*** (0.053)*** (0.076)*** (0.076)*** (1.174)*** (1.166)*** (1.335)*** (1.336)*** tmall 0.255 0.303 0.402 2.530 -1.636 2.117 2.468 -81.721 (0.085)*** (0.085)*** (0.121)*** (3.908) (0.670)** (0.715)*** (0.892)*** (41.888)* shipfee -0.003 -0.003 -0.070 -0.070 (0.000)*** (0.000)*** (0.007)*** (0.007)*** credit_card 0.203 0.203 1.023 1.024 (0.040)*** (0.040)*** (0.390)*** (0.389)*** cam_num -0.004 -0.004 -0.043 -0.043 (0.001)*** (0.001)*** (0.008)*** (0.008)*** prepay 0.001 0.001 0.003 0.003 (0.000)*** (0.000)*** (0.000)*** (0.000)*** store_dur 0.005 0.005 0.007 0.007 (0.001)*** (0.001)*** (0.007) (0.007) rate1tmall -0.439 17.479 (0.806) (8.695)** _cons -5.409 -0.514 6.661 6.616 -116.975 -105.106 -30.722 -30.029 (0.997)*** (1.075) (1.526)*** (1.528)*** (25.112)*** (25.425)*** (28.601) (28.602) R 2 0.00 0.01 0.03 0.03 0.00 0.04 0.08 0.08 N 475,403 475,403 355,962 355,962 47,248 47,248 38,393 38,393 * p< 0.1; ** p< 0.05; *** p< 0.01 19 Table 2.5: Effect of Ratings on Sales: fixed effect sales sales sales sales sales sales sales sales lprices -0.945 -2.016 -2.453 -2.453 -2.330 -11.752 -12.964 -12.942 (0.051)*** (0.113)*** (0.155)*** (0.155)*** (0.555)*** (1.278)*** (1.662)*** (1.662)*** rate_1 6.066 -0.237 -0.354 -0.354 75.061 -7.962 -7.955 -7.146 (0.451)*** (0.473) (0.598) (0.598) (10.679)*** (18.253) (20.343) (20.352) rate1sq -0.848 0.039 0.058 0.058 -9.866 1.213 1.335 1.208 (0.053)*** (0.057) (0.074) (0.074) (1.166)*** (2.017) (2.282) (2.284) tmall 0.303 0.343 0.434 0.494 2.117 2.251 2.489 -56.557 (0.085)*** (0.066)*** (0.089)*** (3.050) (0.715)*** (0.726)*** (0.877)*** (44.300) rate1tmall -0.012 12.266 (0.629) (9.201) _cons -0.514 18.511 23.082 23.082 -105.106 117.855 130.386 129.269 (1.075) (1.417)*** (1.868)*** (1.868)*** (25.425)*** (43.336)*** (48.689)*** (48.695)*** R 2 0.01 0.75 0.76 0.76 0.04 0.76 0.76 0.76 N 475,403 475,403 355,962 355,962 47,248 47,248 38,393 38,393 * p< 0.1; ** p< 0.05; *** p< 0.01 20 Table 2.6: Effect of Quality Signals on Sales: IV sales sales sales sales lprices_hat -0.425 -0.928 -1.201 -1.201 (0.050)*** (0.068)*** (0.094)*** (0.094)*** rate_1 5.087 6.068 2.772 2.782 (0.454)*** (0.451)*** (0.643)*** (0.643)*** rate1sq -0.697 -0.848 -0.409 -0.409 (0.054)*** (0.053)*** (0.076)*** (0.076)*** tmall 0.247 0.303 0.404 2.532 (0.085)*** (0.085)*** (0.121)*** (3.909) rate1tmall -0.439 (0.806) _cons -3.847 -0.662 5.941 5.897 (1.097)*** (1.144) (1.633)*** (1.635)*** R 2 0.00 0.01 0.03 0.03 N 475,403 475,403 355,962 355,962 * p< 0.1; ** p< 0.05; *** p< 0.01 Table 2.7: Effect of Quality Signals on Sales: FE and IV sales sales sales sales lprices_hat -0.928 -0.965 -1.118 -1.118 (0.068)*** (0.336)*** (0.448)** (0.448)** rate_1 6.068 -0.228 -0.367 -0.367 (0.451)*** (0.473) (0.599) (0.599) rate1sq -0.848 0.038 0.060 0.060 (0.053)*** (0.057) (0.075) (0.075) tmall 0.303 0.346 0.433 0.505 (0.085)*** (0.066)*** (0.089)*** (3.051) rate1tmall -0.015 (0.629) _cons -0.662 9.337 11.145 11.144 (1.144) (3.106)*** (4.203)*** (4.203)*** R 2 0.01 0.75 0.76 0.76 N 475,403 475,403 355,962 355,962 * p< 0.1; ** p< 0.05; *** p< 0.01 21 Table 2.8: Effect of Prices on Other Markets on Prices: first step in IV lprices lprices lprices lprices pdifavg 1.426 1.080 1.084 1.084 (0.006)*** (0.001)*** (0.002)*** (0.002)*** rate_1 -0.994 -0.058 -0.031 -0.031 (0.035)*** (0.009)*** (0.011)*** (0.011)*** rate1sq 0.157 0.008 0.005 0.005 (0.004)*** (0.001)*** (0.001)*** (0.001)*** tmall -0.045 -0.005 -0.013 0.020 (0.007)*** (0.002)*** (0.002)*** (0.065) rate1tmall -0.007 (0.013) _cons 9.837 8.809 8.784 8.783 (0.077)*** (0.019)*** (0.023)*** (0.023)*** R 2 0.13 0.95 0.95 0.95 N 475,403 475,403 355,962 355,962 * p< 0.1; ** p< 0.05; *** p< 0.01 Table 2.9: Effect of Prices on Other Markets on Prices: first step in FEIV lprices lprices lprices lprices pdifavg 1.080 0.488 0.514 0.514 (0.001)*** (0.002)*** (0.003)*** (0.003)*** rate_1 -0.058 -0.001 0.015 0.015 (0.009)*** (0.007) (0.007)** (0.007)** rate1sq 0.008 -0.000 -0.003 -0.003 (0.001)*** (0.001) (0.001)*** (0.001)*** tmall -0.005 -0.002 0.001 0.008 (0.002)*** (0.001)*** (0.001) (0.037) rate1tmall -0.001 (0.008) _cons 8.809 8.729 8.956 8.956 (0.019)*** (0.014)*** (0.015)*** (0.015)*** R 2 0.95 0.99 0.99 0.99 N 475,403 475,403 355,962 355,962 * p< 0.1; ** p< 0.05; *** p< 0.01 22 Table 2.10: Effect of Quality Signals on Sales Probability psales psales psales psales lprices -0.022 -0.089 -0.112 -0.112 (0.001)*** (0.002)*** (0.002)*** (0.002)*** rate_1 0.386 0.414 0.188 0.192 (0.014)*** (0.014)*** (0.018)*** (0.018)*** rate1sq -0.051 -0.055 -0.024 -0.024 (0.002)*** (0.002)*** (0.002)*** (0.002)*** tmall 0.056 0.060 0.076 0.980 (0.003)*** (0.003)*** (0.003)*** (0.109)*** shipfee -0.000 -0.000 (0.000)*** (0.000)*** credit_card 0.044 0.044 (0.001)*** (0.001)*** cam_num -0.000 -0.000 (0.000)*** (0.000)*** prepay 0.000 0.000 (0.000)*** (0.000)*** store_dur 0.001 0.001 (0.000)*** (0.000)*** rate1tmall -0.187 (0.022)*** _cons -0.376 0.163 0.650 0.631 (0.031)*** (0.033)*** (0.042)*** (0.043)*** R 2 0.01 0.03 0.08 0.08 N 475,403 475,403 355,962 355,962 * p< 0.1; ** p< 0.05; *** p< 0.01 23 Table 2.11: Effect of Quality Signals on Sales Probability: FE psales psales psales psales lprices -0.089 -0.124 -0.156 -0.156 (0.002)*** (0.005)*** (0.006)*** (0.006)*** rate_1 0.414 0.000 -0.005 -0.005 (0.014)*** (0.020) (0.022) (0.022) rate1sq -0.055 0.001 0.001 0.001 (0.002)*** (0.002) (0.003) (0.003) tmall 0.060 0.051 0.057 0.737 (0.003)*** (0.003)*** (0.003)*** (0.115)*** rate1tmall -0.140 (0.024)*** _cons 0.163 1.165 1.555 1.548 (0.033)*** (0.059)*** (0.070)*** (0.070)*** R 2 0.03 0.56 0.58 0.58 N 475,403 475,403 355,962 355,962 * p< 0.1; ** p< 0.05; *** p< 0.01 24 Chapter 3 Seller’s Management of Rating Scores through Dynamic Pricing abstract Rating scores help sellers to achieve better market performance, but seller’s rating scores management is less studied. This paper takes advantage of a unique identification opportunity provided by the rating score system on Taobao, China’s largest trading platform, to study seller’s management of rating scores. Since accumulation of rating scores on Taobao requires both good reviews per purchase and trade volumes, sellers can accelerate the rating scores accumulation through boosting trade volume by cutting prices. First, I construct a dynamic pricing model to describe seller’s incentive to manage rating scores. The incentive to manage the rating scores depends on two key elements: (1) buyers’ willingness to pay for high rating scores and (2) how trade volumes affect the speed of accumulation. Then, using a transaction data set over time from Taobao, I structurally model and estimate these two key elements. The seller’s heterogeneity and time trend of prices is also addressed. The model is estimated with a nested fixed point algorithm similar to Rust (1987). The estimation results show seller’s ability to manage rating scores: 10sales increase the probability of achieving higher rating scores by 2-4 percentage points. However, the effect of rating scores on sales is small and not significant, especially when ratings are at low levels. As a result, from counter factual analysis, if there were no rating scores management, the prices will be .1 - 1% higher. 25 3.1 Introduction Evaluation from peer consumer group helps consumers to better learn product/service qual- ity when they make purchasing decisions. When consumers buy products on trading plat- forms such as Amazon and eBay, they face many anonymous sellers with little information to learn their trustworthiness. The lack of information may hinder transaction on the platform (Akerlof, 1970). To solve the information asymmetry, platforms have introduced various mechanisms aiming to reveal the reliability of their participating sellers. One commonly pro- vided mechanism is a rating score system: platforms encourage previous purchasers to rate their purchasing experience. The ratings are aggregated into scores and displayed on seller’s introductory page as a quality signal. Many studies on eBay confirmed the effectiveness of this rating score system. Sellers with high rating scores have a higher chance of sales and a higher transaction price when a transaction happens. 1 The effect is not limited to trading platforms for physical consumption products, but is also found for other products and on independent third party websites, such as reviews on yelp for restaurants profitability (Luca, 2012; Anderson and Magruder, 2012), reviews on Yahoo! Movie for movie box office per- formance (Duan, Gu, Whinston, 2008), and bestseller list on Amazon and Barnes and Noble for book sales (Chevalier and Mayzlin, 2006). While the studies mostly focused on the demand side, there is less evidence on the supply side about how sellers react to the rating score system. If the mechanism is indeed effective so that sellers with higher rating scores enjoy a higher profit, rational sellers should notice the premium and have incentive to manage their rating scores. Indeed, some indirect evidence of manipulation is documented in other contexts, such as Mayzlin et al. (2014) and Luca and Zervas (2013). In the case of trading platform, sellers should have an even higher incentive to manage rating scores. As small anonymous sellers, they rely on the rating scores as their main reputation signal to differentiate themselves. Failure to consider the seller’s reaction to 1 See Cabral, Hortacsu (2010) for a recent work. For survey of earlier work, see Dellarocas (2006) and Bajari and Hortacsu (2003). 26 the existence of feedback mechanism will bias the estimation of the rating score premium. For example, a simple regression may over or under estimate the effect of rating scores, as seller’s attempt to manage rating scores affect both ratings scores and observed market outcomes. The regression discontinuity method fails as the incentive to manipulate rating scores differs on the two sides of the thresholds. 2 A better way to evaluate the rating score premium is to take the seller’s reaction into consideration. That is the goal of this work. Among this trend of literature, I structurally estimate the rating score premium and seller’s incentive to manage their rating scores jointly, by exploiting the rating score accumulation rule on Taobao.com (Taobao afterward), the biggest trading platform in China. Taobao has a unique cumulative rating score system: for each successful transactions, the seller receives an evaluation based on overall shopping experience, categorized into positive, neutral or neg- ative. The rating score is calculated as the total number of positive ratings minus the total number of negative ratings. The rating scores are iconized and displayed in a prominent place on the seller’s introductory page. 3 Since the rating scores are accumulative, sellers can rise their rating scores faster if they are able to achieve more transactions. In principle, a seller can set his prices at lower level so that he can get more sales to build up his rating scores, and then take advantage of the high rating scores in the future. Such incentive depends on the value of the rating scores, how trading volumes affect the speed of accumulation, as well as competition from other sellers. The hypothesis is illuminated formally in a dynamic pricing model. I begin with a sin- gle agent model in which sellers determine their prices based on their own rating scores and 2 In papers using RD method, such as Luca (2012) and Anderson and Magruder (2012), they argue such manipulation is not common in the Yelp case under their studies. In other circumstances, this is not the case. In another work, using the same dataset used in this paper, I illuminate the possible existence of seller’s manipu- lation and the failure of RD. When ratings are from previous sales, efforts to accelerate rating accumulation on the left of the threshold create a hump on the left. And as incentive is smaller after crossing the threshold, the expected jump is dampened if not reversed. Both the two effects make the regression discontinuity results less reliable. 3 Described in more details in the background and data description. 27 private states as well as market characteristics. Sellers compete for demand both for con- temporaneous profit and the chance to build up their rating scores. The equilibrium pricing is described by a Markov Perfect Equilibrium, in which the rating scores affect prices and sales, while the prices and sales affect next period rating scores by the rating scores accumulation rule. Compared to static pricing, sellers set prices more aggressively, especially when the rating scores are at low levels. Such incentive is stronger when the rating score premium is higher or rating score accumulation is easier. The intuition is empirically tested using a unique dataset from Taobao. The data used in the paper are panel data of sellers selling digital single-lens-reflex cameras (SLR) from September 2011 to April 2013, including transaction volume and prices, seller’s rating scores and other characteristics. The dataset contains more than 100 different camera models. For each camera model, depending on its popularity, there are tens to hundreds of sellers com- peting on the platform. The model is compromised to better fit the data. First, as is typical for online sales, the sales data display a large dispersion: most sellers have zero or very few sales, while a small fraction of sellers occupy a large fraction of market share, implying large heterogeneity among the sellers. I use a mixture model to allow for heterogeneity in seller’s popularity. Second, as is also typical for digital products, the overall prices of the product decline over time. To control the time trend, the age of the product is included in the demand and marginal cost. Doing so also help to approximate possible dynamics considerations in demand (see the work of Lou et al., 2008). The model is estimated using a nested fixed point algorithm similar to Rust (1987). Specifically, for a given set of parameters, I solve the dynamic pricing process described in the model. The optimal prices are determined given the parameters. Then I choose market parameters to match the model predicted prices to the prices observed in the data. So the algo- rithm contains two loops: in the inner loop, I solve the dynamic programming given a certain set of market parameters. In the outer loop, I use maximum likelihood to maximize the prob- ability that the market predicted prices match observed prices in the data. The consistency 28 of the estimator is guaranteed by the MLE in the second step. The computational burden is to solve the dynamic programming problem repeatedly. To make the model computationally feasible, The demand specification is deliberately chosen so the dynamic programming can be solved easily. The estimation results confirmed seller’s management of rating scores. For 10% increase of sale, the probability of rating scores moving to a higher group increases by 2 to 4 per- centage points. Consumers are willing to pay more for sellers of high rating scores, but only when the rating scores are high enough. Counter factual analysis shows that the prices will be .1-1% higher if there are no rating scores dynamic concerns, indicating sellers do give a small discount to attract ratings. Then I extend the model to allow for strategic interaction of prices among sellers. I employ the concept of Oblivious Equilibrium (OE) to solve the high dimension problem raised from large number of sellers. In the OE, sellers make sub-optimal pricing decision by responding to long-run average of market conditions, and the market condition is consistent to their decisions in equilibrium. The model findings are similar to the single agent model. As number of sellers increases, the prices drop due to more competition. The dynamic prices (optimal pricing with rating score consideration) drop slower compared to static prices (opti- mal prices without rating score consideration). Seller’s incentive to manage rating scores is weaker as achieving sales is harder with more competition. Besides, sellers are allowed to differ in their ability to attract good ratings. Buyers endoge- nously determine the rating score premium by inferring the fraction of High type sellers (who are more likely to get good ratings) from rating scores. In reaction, High type sellers have higher incentive to manage their rating scores by pricing more aggressively. As a result, sell- ers with high rating scores are more likely to be High type sellers, and consumers are willing to pay a premium for that. In this way, I show the rating scores system can efficiently separate sellers, at least in the long run. 29 The rest of the paper is organized as follows: section 2 is the literature review; in section 3, I introduce the data and describe data patterns; section 4 presents the dynamic pricing model and model prediction; in section 5, I estimate the model and do the counter-factual analysis; in section 6, I extend the model to allow strategic interaction and seller’s heterogeneity of getting good ratings. Last section is conclusion and discussion of future work. 3.2 Literature Review There is growing evidence that consumers are influenced by rating scores online, either from the trading platform or from a third party review website. Earlier studies look at the effect of ratings on eBay. Bajari and Hortacsu (2003) and Dellarocas (2006) provides summaries of the effect of feedback on eBay. In the works of Resnick and Zeckhauser (2002), Houser et al. (2006), Resnick et al. (2006), and many others, they find positive correlation between the price of an item and the feedback that a seller has received on eBay. Most of the works use cross-sectional data, except Cabral and Hortacsu (2010). Some papers do not discuss the endogeneity of feedback explicitly. Some works use experiment to guarantee exogeneity, for example in Resnick et al. (2006). The discussion of endogeneity focuses on the omitted variable bias, as intrinsic quality affect both market performance and rating scores received. The seller’s management of rating scores certainty adds more dimension of possible endo- geneity, but is less discussed in these works. The exception is Cabral and Hortacsu (2010). In their work, thanks to the panel data structure and detailed information on feedback, they document price adjustment right after a negative rating is presented. They show sales decline once the sellers have received negative ratings, and sellers are more likely to give a discount accordingly as a reaction to regain the market. More evidence is accumulated in other context to answer the general question of how to evaluate the value of the information from peer review. And the endogeneity of rating scores is taken care of more carefully, mostly using program evaluation methods. Among 30 all the studies, Jin and Kato (2005) use experiments to look at the intervene of price, quality and seller reputation in Internet auctions. Duan, Gu and Whinston (2008) estimate the joint determination of new movie’s book office revenues and the online reviews using simultane- ous equation models. They show the positive effect of ratings are gone once the endogeneity is controlled. Chevalier and Mayzlin (2006) look at the effect of book reviews on the book sales. They use the difference of reviews and sales on two main online markets, Amazon and Barnesandnoble, to control the effect of book’s true quality, so the method is similar to a difference in difference method. Luca (2012) and Anderson and Magruder (2012) use regres- sion discontinuity and show switching from four stars to four and half stars on Yelp helps restaurants to make higher profits. All these studies discuss the endogeneity of rating scores from the missing observation of product quality. Indeed, at least in the work of Chevalier and Mayzlin (2006), Luca (2012) and Anderson and Magruder (2012), the identification relies on the assumption that there is no seller’s manipulation of rating scores. We need to reconsider the estimation if we believe that seller’s manipulation of rating scores is a potential possibility to make the ratings endogenous. In theory, economists have discussed whether the rating score manipulation affect the informativeness of the rating scores. For example, Dellarocas (2006) shows strategic manip- ulation can in theory increase or decrease the informativeness of online reviews. Besides, when the ratio of honest ratings are high enough, strategic manipulation is too costly for the sellers. However, a few indirect empirical evidences of rating scores manipulation show neg- ative results. Mayzlin et al. (2014) compare reviews on two travel websites: Expedia (who only accepts reviews from customers) and TripAdvisor (who accepts reviews from anyone), and find higher ratio of high ratings for single-unit owner hotels, and higher ratio of low rat- ings for their competitors on the latter sites. That is a hint that small hotel owners could have posted fraud review for themselves and their competitors. Luca and Zervas (2013) have doc- umented fraud in posting reviews on Yelp: they find roughly 16 percent of restaurant reviews on Yelp are identified as fraudulent, and tend to be more extreme (favorable or unfavorable) 31 than other reviews”. Restaurants are more likely to post fraudulent reviews when they have few reviews or bad reviews, and are more likely to post unfavorable reviews for competitors when facing increased competition. The idea of pricing in the presence of learning is not new. The early works go back to Bergemann Valimaki (1996, 1997). Among the literature of reputation, the works by Cabral (2005), Fisherman & Rob (2005), Bar-Isaac and Tadelis (2008) discuss the reputation concern in various contexts. My paper adopts their idea in the frame of seller’s strategy under the rating scores system on online trading platforms. The most relevant studies to my paper are Saeedi (2014) and Fan, Ju and Xiao (2014). Both papers are about the seller’s dynamic decisions on a trading platform. In Saeedi (2014), she looks at the dynamics of seller’s “powerseller” status and “registered store” status as two signals of quality. To maintain the two status, the sellers have to satisfy a quality standard and a quantity standard. The dynamic model is estimated using two-step estimators proposed in Bajari, Benkard and Levin (2007). The use of the BBL method requires some restrictions on seller’s heterogeneity and time trend. Specially, Saeedi assumes that the sales (policy function in the dynamic programming) follow Negative Binomial distribution, which is not guaranteed from the model. Despite the limits in estimation, the estimation results confirm that reputation has a positive effect on the expected profits of high-quality sellers, as well as on their market share. Remove the signals will eventually harm the market. Fan, Ju and Xiao (2014) also look at the seller’s management of rating scores on Taobao, using a 25% random sample on the platform between March 2010 and April 2011. My paper differs from theirs in sereval ways: first, the papers measure seller’s rating score management differently. Fan, Ju and Xiao (2014) shows opposite sign of ratings-sales correlation between new sellers and established sellers, and also shows the incentive to set lower prices when rating scores threshold is near is stronger for new sellers. In my paper, I measure the incentive to manage rating scores by to what degree a seller is willing to cut prices for rating scores accumulation, and relate the incentive to the rating scores’ effect on sales. Second, they use a reduced 32 form estimation with instruments, while I use a structural method. Potentially, I can show the mechanism more explicitly and do more counter factual analysis. Last, the data set is different. Fan, Ju and Xiao (2014) use product’s aggregated revenue and transactions in the analysis, so they can only approximate the prices from revenue and transaction volume. As a result, it cannot say too much on the effect of pricing or competition. 3.3 Background and Data Background The online trading platform I focus on is Taobao.com, China’s biggest consumer-to-consumer trading platform. The platform occupies 90% of the c2c market by the end of 2012. The operation mode of Taobao is similar to eBay: it is a platform that links sellers and buyers, and profits from advertising and providing service to the sellers. It does not sell as a direct merchant like what Amazon does. Like Amazon, most of the products sold on the platform are first hand, and are sold by a list price set by sellers, rather than by an auction. Taobao, together with Tmall.com, another trading platform owned by the Alibaba group, dominates the Chinese e-commence market. The platform is Titanic in terms of both users and trading volumes: Alibaba has a total of 8 million active sellers and over 230 million active buyers on its platform. In 2013, Taobao and Tmall handled $240 billion in sales. That’s double the size of Amazon, and triple the size of eBay. 4 Like any other trading platforms, Taobao designs ways to gather and publicize informa- tion that reveals sellers’ reliability in constructing the platform. As one of the measures, Taobao provides a decentralized rating score system. Buyers are asked to give ratings and reviews on their past purchasing experience, based on the quality of the product, shipping 4 the numbers can be found at http://www.businessinsider.com/alibaba-facts-size-growth-ipo-2014-9, or Alibaba’s roadshow slides that were presented on its IPO Eve. http://www.slideshare.net/pierrepoignant/alibaba-roadshow-presentation 33 speed, and services in the transaction. The ratings are of three kinds: positive, neutral, and negative. One special rule is that if buyers do not submit their rating within a month from purchase, the default is positive, rather than neutral. The aggregation rule is that: positive rating counts one point, negative rating counts minus one point, and neutral rating counts zero point. The rating score for the seller is the total number of postie ratings minus the total number of negative ratings. For example, if a seller receives 90 positive ratings and 10 nega- tive ratings out of 100 transactions, his rating scores add 80. The rating scores are displayed on the sellers’ introduction page, iconized as numbers of hearts, diamonds or crowns. The default icon is hearts. If the rating scores are above 250, the icon is promoted to diamonds; if the rating scores are above 10000, it is promoted to crowns. The standard is public and can be found on the website easily so consumers are fully aware of the meaning of hearts, diamonds and crowns. (See Table 1) Data Description The data used in the paper are panel data of sellers selling digital single-lens-reflex cameras (SLR) from September 2011 to April 2013, including transaction volumes, prices, seller’s rating scores and other characteristics. The data are collected using a Python web-scrapping program on a monthly base. I collect all quantifiable information regarding the seller and the product, in an attempt to approximate the information a typical consumer will have when she makes purchasing decisions. Non-quantifiable information such as textual comments is not included due to technique limitation of machine-reading these comments. I choose durable products for the demonstration for the following reasons: First, cameras are valuable goods such that buyers care its quality more as compared to small items like, for example, UV filters. Second, buyers are less likely to be returning customers, eliminating the probability that buyers having more information about the sellers by repeated purchase. Third, consumers are more likely to agree on the quality of durable products, and the evaluation is less likely be mixed with personal tastes of the product. Last, camera model is a well defined product, 34 which helps to collect data and to define competitors. For example, a search for ’Canon 550d’ camera is more definite than searching for ’Nike running shoes, red’. The data contain more than a hundred different kinds of camera models, after combining camera-lenses bundles and other proper data cleaning. Table 3.1 lists the description of the market by each month. Depending on the popularity of the camera model, the number of sellers ranges from several to more than one thousand sellers. On average, there are over two hundred sellers for one camera model. The distribution of sales is also skewed: the most popular models can sell around 3000 units per month, while the niche ones sell around 10 units per month. The mean median prices for the cameras are 6000 - 7000 yuan (around 1000 - 1200 dollars). Table 3.2 lists the total number of sellers. In each month, there are around 1300 - 1400 sellers selling cameras on Taobao. The sellers are further divided into 6 groups based on their rating scores. The fraction of each group does not vary much across months, implying no clear evidence of rating scores inflation on the market. Table 3.4 shows Table 3.1: Data Description period Camera models number of sellers total sales median prices avg max min avg median max avg max min 1 84 232.62 1280 5 167.33 11 2655 6678.66 51900 1350 2 93 233.92 1459 8 122.72 10 1889 6146.88 53000 1150 3 99 215.23 1142 8 120.12 9 2302 6397.05 53750 1210 4 92 228.92 1303 8 138.95 9.5 2743 6593.26 53000 980.1 5 89 221.87 1207 8 115.71 8 2517 6696.79 52000 1000 6 96 207.07 1108 9 143.31 7 3151 6825.82 49900 950 7 94 217.07 1233 7 158.20 15.5 2737 6901.75 47000 850 8 94 224.31 1236 4 173.53 15 3543 6504.98 45900 850 9 91 228.42 1255 7 163.91 14 3062 6690.38 45500 851 10 97 249.84 1584 8 152.88 8 2937 6894.33 51042.5 850 11 97 260.02 1651 6 161.84 13 2720 6747.59 49000 850 12 95 276.65 1681 4 181.92 15 3586 6441.08 45100 850 13 93 204.56 1205 4 22.61 9 164 6683.41 45000 850 the positive correlation of rating scores and sales by comparing the monthly sales of heart, 35 Table 3.2: Distribution of Rating Scores period Number of Distribution of sellers rating scores (%) sellers 1 2 3 4 5 6 1 1197 22.14 20.63 23.14 10.36 16.54 7.18 2 1342 22.13 20.72 24.74 10.73 15.35 6.33 3 1403 22.02 22.17 24.59 10.19 15.82 5.20 4 1478 23.75 21.85 23.21 10.35 15.63 5.21 5 1442 20.25 23.09 20.94 11.51 18.24 5.96 6 1434 21.69 22.32 23.08 11.30 16.11 5.51 7 1491 22.54 22.74 22.54 11.07 15.69 5.43 8 1503 21.76 22.55 22.36 11.04 17.03 5.26 9 1484 18.26 23.32 22.24 11.59 18.33 6.27 10 1472 18.48 22.96 23.37 11.07 18.48 5.64 11 1404 16.95 23.79 24.72 10.54 18.38 5.63 12 1367 16.17 23.77 24.51 11.41 18.29 5.85 13 1117 16.74 23.81 22.65 11.19 19.70 5.91 diamond and crown sellers. Only 5 percent of heart sellers realize sales, while the fraction for diamond and crown sellers are around 10% and 30% respectively. The effect are not causal, as crown sellers can be better in other dimensions not displayed here. Besides, it is possible that the relationship is inverse, as accumulation of rating scores to be a diamond/ crown seller requires realization of large sales. For those sellers who have realized sales, average sales of diamond and crown sellers are higher than that of heart sellers. The average sales for heart sellers are 2 units and that for diamond and crown sellers are 5 and 20 units respectively. There is also large inequality of sales within the groups. Table 3.3: Transition of Rating Scores rating score in t 1 2 3 4 5 6 1 88.09 2.32 0.56 0.20 0.13 0.07 2 10.09 89.78 1.50 0.08 0.12 0.08 rating score 3 1.13 7.36 89.39 6.02 0.11 0.03 in t+1 4 0.18 0.21 7.93 81.32 2.98 0.00 5 0.46 0.25 0.60 12.38 95.09 3.01 6 0.05 0.08 0.01 0.00 1.56 96.80 36 Figure 3.1: Rating Score Distribution over Time Table 3.3 shows the movement of rating scores. The rating scores are divided into six categories and the table lists the fraction of settling in each category in the next month. When rating scores are low, around 90% of sellers remains in the same category. The fraction is as high as 95% for sellers with high rating scores. And the fraction of moving up is higher than that of moving down, especially when the rating sores are low, indicating sellers are more likely to get positive ratings than negative ratings. It raises the concern that rating scores may be inflated as time goes by. Figure 3.1 shows it is not the case in the short run. Figure 3.1 displays the fraction of sellers in each category and there is no clear declining tendency for the fraction on the low end, nor increasing tendency for the fraction on the high end. The fraction of each category remains relatively constant in the sampling period. Figure 3.2 and 3.3 shows the time pattern of prices and sales respectively. Figure 3.2 plots the median prices of three Canon’s entry-level cameras and Figure 3.3 plots the total sales. The three cameras are Canon 550D, 600D and 650D. They are of the same series, launched 37 Table 3.4: Correlation of Rating Scores and Sales Period Prob(sales> 0) Mean of sales for sales> 0 Hearts Diamonds Crowns Total Hearts Diamonds Crowns Total 1 7.53 9.25 25.34 9.57 1.94 4.88 26.50 7.46 2 6.43 8.21 27.04 8.44 1.75 4.28 21.29 6.24 3 7.53 9.96 28.96 9.96 1.72 4.79 16.57 5.62 4 6.49 9.83 28.99 9.42 1.74 5.41 18.83 6.46 5 5.72 8.43 23.33 8.27 1.58 4.15 20.54 6.29 6 5.83 11.41 29.10 10.07 1.63 4.94 22.00 6.92 7 5.89 12.85 29.91 10.93 1.99 5.21 19.40 6.72 8 6.03 12.86 32.52 11.03 2.08 5.42 20.86 7.08 9 5.51 12.84 31.33 11.03 2.07 4.23 19.84 6.51 10 4.31 11.41 33.70 9.23 1.87 4.69 19.51 6.67 11 3.91 11.52 33.45 8.76 1.86 4.61 23.21 7.17 12 3.41 10.86 34.90 8.22 2.07 4.71 26.03 8.06 13 2.95 7.33 17.33 5.46 1.91 2.12 3.62 2.22 Total 5.32 10.56 29.28 9.25 1.86 4.68 20.79 6.60 in Feb. 2010, Feb. 2011, and May 2012 respectively. 5 There is a clear tendency in the price drop. The price drops 300 - 500 Yuan (or around 10 - 15% of the prices) in around a year for older models. The tendency in sales is less clear. Besides, cameras has a long product life cycles: after the introduction of a new model, the sales of older models can be still pretty high. Figure 3.4 shows the heterogeneity in sales. Figure 3.4 plots the Lorenz curve for the sale of Canon 550D. The x-axis is the fraction of sellers ordered by ascending sales, and the y-asis is the fraction of total sales (market share) from these sellers. If each seller sells the same unit of cameras, the curve is a 45 degree line. From Figure 3.4, the top 10% sellers occupy around 80% of the market share, while the bottom half sellers occupy only around 5% of the market. The winner-takes-all pattern is very typical for sales online, being known 5 New models have some technical improvement in some features, but they have the same targeting market of entry level non-professional market. Since they are of the same series, similar to iPhone 4, 5 and 6, so I treat them as directly comparable. 38 Figure 3.2: Prices Age Relationship Figure 3.3: Sales Age Relationship 39 Figure 3.4: Seller’s Inequality in Sales as the Pareto principle or “80-20” rule. 6 I allow for seller’s heterogeneity of popularity in the estimation model to help to predict the pattern. 3.4 Model Basic Model The model describes the seller’s incentive to manage his rating scores, given consumer’s evaluation of rating scores and the rule of rating score revolution. I show how sellers set prices more aggressively to affect their rating scores. At each time period t, seller j has a rating score x jt accumulated from previous sales. The rating scores are categorized into groups. With a little abuse of notation, let the groups be fx 1 ;:::;x K g. Let number of sellers whose rating score level is in the group of x k be s kt 2N , 6 http://en.wikipedia.org/wiki/Pareto_principle 40 then the vector s t =fs 1t; :::s kt; :::;s Kt g2 S N K captures the rating score distribution on the market. Products differ in their popularity so the number of sellers and their rating scores distribution for each product are different. Consumers choose sellers based on prices and rating scores. In particular, for seller j at time period t, his demand is determined by a linear demand function d jt =g o + å k g xk 1(x jt = x k )g p p jt +g z z t +e jt (3.1) In the equation, x jt is the rating score, p jt is the price, and z t is other market conditions including the average prices and the rating score distribution of his competitors on the market. e jt is the shock, and is independent across seller, product and period. I assume the shocks follow a normal distribution N(0;s 2 e ). The contemporaneous profit is p jt =(p jt c jt )d jt where c t is the marginal cost for the product at the age t. I assume c jt = c+h jt where c is a constant and h jt is shock on cost. The shock is independent across seller, product and period, and is orthogonal to the demand shocke jt . Also, I assumeh jt follows a normal distribution N(0;s 2 h ). The sales in the current period affect both the contemporaneous profit as well as the rating scores in the next period. Specifically, let x jt+1 = f(x jt ;d jt ), where function f should be increasing in both the two augments and concave in the second augment. In particular, I assume that the transitional matrix takes the form of x jt+1 j(x it ;d jt )= 8 > > > > > < > > > > > : x jt + 1 a 1k + b 1k log(d jt ) x jt with prob a 0k + b 0k log(d jt ) x jt 1 a 2k + b 2k log(d jt ) (3.2) 41 where x it = x k . The sum of a is 1 and the sum of b is 0 from the property of transition probability. When x jt takes the maximal possible value, a 1K and b 1K are zero. Similarly, when x jt takes the minimal possible value, a 21 and b 21 are zero. The demand is not influential enough to lead the probability out of[0;1], so the bound condition is not discussed. The probability of transiting to a higher rating scores depends on the current rating scores and the realized sales. The hypothesis is that having realized more sales will move the dis- tribution of rating scores to the higher group more likely, and the hypothesis is verified in estimation. The functional form is chosen for convenient and calculation simplicity to solve the dynamic programming. A more flexible form (for example, kernel estimation of condi- tional density) should also be tractable. Notice the seller’s problem is modeled as a single agent’s problem. When seller j makes his pricing decision, he relies on the information of his own states and the market conditions. The market conditions are exogeneously given and the seller j’s decision has no influence on these conditions. The setting fits the environment for empirical study as there are many sellers for a given product. A byproduct benefit is that the model avoids arbitrary restriction on seller’s information of other competitors. In the single agent model, other competitor’s prices do not directly appear in seller j’s demand or pricing decision making. That comes from seller j’s lack of information of its competitor’s conditions. Since there are many small sellers on the market, it is too costly for seller j to track its competitors and adjust pricing accordingly in real time. Instead, seller j only focuses on its own state and the market distribution that summarize his competitor’s states. By doing so, seller j does not need to learn the exact rating scores of all the competitors, nor to learn competitors’ sales in order to track their rating scores transition. All the seller j needs to know is the average of the market conditions. The single agent model does not mean that there is no competition and the agent acts like a monopoly. The demand is constrained by the average prices, number of competitors and the rating scores distribution. 42 Seller j chooses the prices at each period to maximize his life-time expected profits, E s;eå t=t b tt p(x jt ; p jt ) given the transition rule of x jt . 7 At the beginning of each period, seller j learns the market conditions in the current period including the demand shocke jt and the marginal costh jt , and determines his price accordingly. Then the demand is realized and his states evolve conditional on the realized demand. This decision repeats for each period. The problem can be described by the following Bellman equation: v(x; p;e;h)=p(x; p;e;h)+bE s 0E e 0 ;h 0[v(x 0 ; p 0 ;e 0 ;h 0 )] where z 0 stands for variable z in the next period. Let Ev(x; p) = R v(x; p;e;h)dF(e)dF(h) be the expected life-time profits. Since the shockse;h are independent across time, the above Bellman equation can be written as v(x; p;e;h)=p(x; p;e;h)+bE x 0[Ev(x 0 ; p 0 )] =p(x; p;e;h)+b å x 0 Ev(x 0 ; p 0 )Pr(x 0 jx;d) (3.3) where the Pr(x 0 jx;d) is given by the transitional matrix specified in equation (3.2). Seller j makes pricing decision to maximize the life-time profits. Let the policy function (optimal pricing) be p(x;e;h). Definition. A Markov Perfect Equilibrium is the value function V(x;e;h) and policy function p(x;e;h) such that: 1. p(x;e;h) maximize V(x;e;h) given the transition rule of states defined in (3.2); 2. the value function defined in (3.3) takes its max when the price is p(x;e;h). 7 For notational simplicity, I omitted other demand shifters in the discussion below. Adding the shifters does not change the discussion. 43 The policy function can be determined by its first order conditions: d(x; p;e)+ ¶d(x; p;e) ¶ p(x;e) (p(x;e) mc)+b å ¶Pr(x 0 jx;d) ¶d ¶d(x; p;e) ¶ p(x;e) V(x 0 ; p 0 )= 0 (3.4) The first two terms are the conventional quantity-price trade-off, and the three term cap- tures the rating scores dynamics concern. A discount in price leads to more sales, which leads to higher probability of higher rating scores and future profit. If the distribution of rat- ing scores does not depend on sales ( ¶Pr(x 0 jx;d) ¶d = 0) or the discount factor is zero, the prices are static. The problem can be solved numerically by grinding the states (x;e;h) and using value function iteration. The rating scores x is discrete by model construction. For the shocks e and h, I take values within3s so it covers 99% of the possible values. By setting the discount factorb to zero, I get the static pricing (optimal pricing when sellers do not consider the rating scores dynamics.) I compare the dynamic pricing and the static pricing. Figure 5 shows the comparing by plotting the relationship of rating scores x and expected optimal pricing p(x)= R p(x;e;h)dF(e)dF(h). The dynamic pricing is always lower than the static pricing. When rating scores are low, the dynamic pricing can be 10% lower. When the rating scores are high, the discount is gone. From the figure, seller j chooses to set lower prices to attract more sales when the rating scores are lower, and to set high prices for higher contemporaneous profits when rating scores are high. Figure 6 and Figure 7 compare the optimal pricing when I change the parameter for the rating scores premium and for the speed of rating scores evolution. From Figure 6, when the return to rating scores increases by 50%, the seller’s pricing is lower as compared to the static pricing. When rating scores are low, the prices are 16% lower. The sellers set prices more aggressively when the return to rating scores is higher. Figure 7 compares the prices when trade volumes lead to faster rating scores accumulation. When the probability of rating 44 Figure 3.5: Pricing-Rating Relationship scores moving to a higher level per trade volume doubles, the prices are lower. When rating scores are low, the prices are 20% lower than the static pricing. These two illumination shows that sellers respond to both the return of rating scores and the speed of accumulation. I focus on these two key factors when I carry out the estimation. 3.5 Structural Estimation Model Modification and Identification The basic model assumes a stationary process: for sellers of the same rating scores and shocks and under the same market conditions, the prices should be the same and do not depend on which time period the pricing decision is made. Besides, the model predicts that the difference in sales among sellers of the same rating scores comes from the shocks and the difference should not be persistent as the shocks are assumed to be independent across 45 Figure 3.6: Pricing-Rating Relationship: comparative statics Figure 3.7: Pricing-Rating Relationship: comparative statics 46 time. The model prediction cannot fit the data pattern I have described above. In the data, it is observed that prices are declining over time, and there is large inequality in sales among sellers and the difference is persistent. I modified the demand model to cater to the data patterns. The demand model for estimation is specified as d jt =g 0 g p p jt +g x x jt +g a age t +g z z t +a j +e jt (3.5) where p jt is the prices, x jt is the rating score, age is the product’s age, and z t are other market conditions including the average prices and the rating score distribution of competi- tors. The age of the product is defined as month after its launching. a j is seller j’s fixed effect. Also I assume the marginal cost is declining over time, or c t = c 0 c age t +h jt . Compare to the basic model, I add the linear time trend in demand and marginal cost in the hope of capturing the time trend. Then I add a seller’s fixed effect of popularity to capture the persistence in demand. To make the estimation feasible, I assume a takes two values from(a H ;a L ) and Pr(a=a H jx)= q(x)2[0;1]. I allow the hidden popularity heterogeneity to differ across rating score groups. If one beliefs that sellers of high rating scores are more populous, then q(x) should increase in x. The transitional matrix remains the same as specified in equation (3.2): x jt+1 j(x it ;d jt )= 8 > > > > > < > > > > > : x jt + 1 a 1k + b 1k log(d jt ) x jt with prob a 0k + b 0k log(d jt ) x jt 1 a 2k + b 2k log(d jt ) In particular, I assume the heterogeneity a j only affects the demand, but not the tran- sitional matrix. That is, given the same rating scores, a popular seller is more likely to be chosen than a less popular seller, so the sales are larger. However, conditional on the same 47 sales, a popular seller is no more likely to move to a more favorable rating scores than a less popular seller. The interpretation for the assumption is: the popular sellers are more favored by buyers from some information known to both parties but not known to econometricians, such as textual comments. However, when purchase decisions are made, the hidden informa- tion is gone. The transition probability relates to how buyers rate sellers. The ratings only depend on the purchasing process and utility of using the products, but not the information used for purchasing decisions. To solve the modified model, I cannot use the value function iteration since the model is no longer stationary. Instead, I assume there is a life cycle for the product and the sales of the product last T periods. 8 Within the time period[1;T], define the value of life-time profits as V jt (x jt ; p jt ;a j ;e jt ;h jt )=p(x jt ; p jt ;a j ;e jt ;h jt )+ E x [ T å t=t b tt Ep(x jt ; p jt ;a j )] =p(x jt ; p jt ;a j ;e jt ;h jt )+bE x;e;h V j;t+1 (x jt+1 ; p jt+1 ;a j ;e jt+1 ;h jt+1 ) (3.6) =p(x jt ; p jt ;a j ;e jt ;h jt )+bE x EV j;t+1 (x jt+1 ; p jt+1 ;a j ) where Ep(x jt ; p jt ;a j ) = E e;h [p(x jt ; p jt ;a j ;e jt ;h jt )] is the expected profits, and EV j;t+1 (x jt+1 ; p jt+1 ;a j )= E e;h [V j;t+1 (x jt+1 ; p jt+1 ;a j ;e jt+1 ;h jt+1 )] is the expected value. Then I solve the pricing of the product within the time period[1;T] by standard backward reduction. Assuming a value for V jT+1 , the problem is solvable backwardly from period T until to period 1. At time t, the future value V j;t+1 is known, as the problem can be solved as if it is a static maximization. The prices are determined by its first order conditions: (p jt mc t ) ¶d jt ¶ p jt + d jt +b å ¶Pr(x t+1 jx t ) ¶d ¶d jt ¶ p jt EV t+1 (x t+1 )= 0 (3.7) 8 Here I assume T is fixed. It may be relaxed to allow T to be random. 48 The first two terms are the same as in static pricing determination, and the last term comes from the dynamics: the prices affect demand, thus the probability of future rating scores and future profits. A special case is when demand does not affect the rating score distribution. In this case ¶Pr(x t+1 jx t ) ¶d = 0, then the pricing is the same as static profit maxi- mization. After getting p jt from the first order condition, put it back into the value function (3.6) to get the value V jt . Then the procedure goes to the period t 1. After properly solv- ing the procedure, I getfV jt = V t (x jt ;a j ;e jt ;h jt )g t=1:T and corresponding prices and demand fp jt = p t (x jt ;a j ;e jt ;h jt )g t=1:T andfd jt = d t (x jt ;a j ;e jt ;h jt )g t=1:T , as long as the parameters in the demand (g), marginal cost (c) and the transitional matrix (a;b) are given. Last thing to close the model is how to set the end value EV jT+1 . The usual practice is to take EV jT+1 = 0, assuming the seller exiting the market after the sales of the products. In my specification, I choose EV jT+1 = EV j1 . The rating scores are associated with sellers rather than with products, so the high rating can still be used for the sales of other products as well. After the sales of the current product, the sellers can use the rating scores to sell other similar products, so the value of rating scores carries on. A byproduct of the setting is that the modified model degenerate to the original stationary model if the age effect in demand and marginal cost is zero, so the models are nested. As now the V jT+1 is unknown, solving the model requires a fixed point argument: given any value of V (s) jT+1 , solve the model by backward reduction and getfV (s+1) jt = V t (x jt ;a j ;e jt ;h jt )g t=1:T ; repeat the process for V (s+1) jT+1 = V (s) j1 until convergence is achieved. I take every camera model as separate market, and repeat the above process to get the prices and sales for each camera models. Since the cameras differ in popularity and age, so the total number of sellers and distribution of their rating scores vary. 49 Estimation Method The estimation is carried out using a nested fixed point algorithm similar to Rust (1987). 9 Given the parameters in the demand (g), marginal cost (c) and the transitional matrix (a;b), I solve the pricesfp jt = p t (x jt ;a j ;e jt ;h jt )g t=1:T for each camera models. Denote the model predicted prices and sales as ˆ p t (x jt ;a j ;e jt ;h jt ) and ˆ d t (x jt ;a j ;e jt ;h jt ). As e and h are assumed to be normal distributed with zero mean and variance s 2 e and s 2 h respectively, by multivariate change of variables, we can get the joint distribution of prices and demands as f d;p ( ˆ d; ˆ p) = å a q(ajx) f e;h (e 1 ( ˆ p; ˆ dja);h 1 ( ˆ p; ˆ dja))j(Jja)j, where e 1 ( ˆ p; ˆ dja) and h 1 ( ˆ p; ˆ dja) are reverse functions to back up the demand and marginal cost shocks, and Jja is the corresponding Jacobian defined as Jj a = ¶e 1 ¶ ˆ p ¶h 1 ¶ ˆ p ¶e 1 ¶ ˆ q ¶h1 ¶ ˆ q . All these numbers can be solved numerically. Since the distribution of seller’s type and shocks are assumed to be known, the price-sales distribution f d;p is well defined. To match the prices-sales in the data, let p jt (x jt ) and d jt (x jt ) be the observed prices and sales for seller j whose rating scores are x jt in the data. Put the values in the calculated distribution density, we get f d;p (d jt ; p jt ) for each observation. Then the loss function is defined as L(a;e;hjx; p;q;q)=å j;t ln( f d;p (d jt ; p jt )). Denoteq as all parameters: q =fg;c;a;b;q;sg, whereg are the parameters in demand, c are the parameters in marginal cost,(a;b) are parameters in transitional matrix, and(q;s) are parameters in the distribution of seller’s typea and shockse andh. The whole process is a maximum likelihood estimation, expect the ˆ p t (x jt ;e jt ;h jt ) needs to be solved from a dynamic programming in each iteration. The calculation burden of the estimation lies on solving the dynamic programming repeatedly. The estimation is done in two steps: first I estimate the transitional process separately and the coefficients (a;b). This step can be done directly by MLE, as there are no unobserved factors in its determination. From the transitional matrix, the likelihood function can be written as 9 The term “nested fixed point algorithm” comes the survey paper by Aguirregabiria and Miller (2007) 50 L(x jt+1 jx jt ;d jt ;a;b)= I(x jt = x k ;x jt+1 = x k + 1)ln(a 1k + b 1k log(d jt )) + I(x jt = x k ;x jt+1 = x k )ln(a 0k + b 0k log(d jt )) + I(x jt = x k ;x jt+1 = x k 1)ln(a 2k + b 2k log(d jt )) where I(x) is the indicator function. In the second step, I use MLE defined above to get the rest of the parameters, denoted as q 0 =fg;c;q;s; ˆ a; ˆ b} and the estimator is ˆ q = argmax q 0 L(ejq 0 )= å j;t ln( f d;p (d jt ; p jt )) The consistency of the estimator is guaranteed by the general result for maximum likeli- hood estimators. Results I present and discuss the estimation results in this sub-section. Table 3.5 gives the estimation results for the transitional probability. The rating scores evolve even without sales of the product, as the sellers sell other products as well. When rating scores are low, the rating scores are more likely to move to a higher level. For example, the probability for seller in the rating scores group 1 to move to group 2 is 12%, while it is 1.2% for sellers to move from rating scores group 5 to 6. There is also a probability to move down to a lower group, but the probability is smaller than that of moving up. Sellers can affect the probability of rating scores moving up by realizing more sales. The effect of sales to rating scores moving up is significant for all rating scores. When seller is in the rating scores group 1, if he can realize 10% more of sales, the probability of moving up increases by 4 percentage points. When his rating score is in group 5, the probability increases by 2 percentage points . Also, sellers with 51 Figure 3.8: Prices Fitness more sales are less likely to encounter a rating score moving down, but the effect is much smaller and not significant in most of the cases. Table 3.6 gives the estimation coefficients for the demand. The coefficients for rating scores are mostly positive but not significant. The coefficient for prices is negative and sig- nificant. And the effects of age and average market prices are not significant. It turns out that the most determining factor is only prices and rating scores play a minor role after controlling the seller’s fixed effect. The results are consistent to fierce competition in a free-entry market environment. Figure 3.8 gives the fitness of prices over time for three popular Canon cameras. The observed prices are more fluctuating than model prediction, but model fitting of the price trend is quiet good. For a better comparison, table 3.7 also lists the prices. The prices of Canon 500d drop from 3,600 to 3,000 Yuan in one year time; the prices of Canon 550d drop from 4,200 to 3,700 Yuan; and the prices of Canon 600d drop from 4,600 to 4,000 Yuan. Though the three cameras are of different ages, the trend is similar. The prices all drop 52 Table 3.5: Transition Probability Estimates up down 1 .1216 + .0422 *log(d) (.0063) (.0099) - 2 .0764 + .0259 *log(d) (.0039) (.0026) .0505 + (-.0016) *log(d) (.0061) (.0035) 3 .0689 + .0124 *log(d) (.0035) (.0016) 0.017 + .0008 *log(d) (.0040) (.0018) 4 .0895 + .0434 *log(d) (.0046) (.0033) .0314 + (-.008) *log(d) (.0049) (.0021) 5 .0120 + .0213 *log(d) (.0013) (.0016) .0063 + (-.005) *log(d) (.0012) (.0006) 6 - .0126 + (-.0007) *log(d) (.0018) (.0006) Note: standard error reported. Estimated by MLE. 53 Table 3.6: Demand Estimates s.e. rating score group 2 0.0027 0.0210 group 3 0.0246 0.0218 group 4 0.1400 0.0280 group 5 -1.9800 0.0250 group 6 2.4700 0.0354 prices -1.0200 0.0199 age -0.0601 0.0007 average prices 0.0019 0.0219 around 500- 600 Yuan in one year, or around 50 Yuan per month. The predicted prices differ from observed ones by mostly less than 2%, and capture the trend correctly. Counter-factual analysis Next, based on the structural parameters, I compare the prices with static pricing when sellers do not have rating scores dynamics. To do the first counter-factual analysis, I resolve the problem with a zero discount factor. If sellers have no incentive to manage the rating scores and set prices to maximize current period profits, the prices is .1 - 1.6% higher than the observed prices. Due to a surprisingly negative effect at rating scores group 5, the magnitude is not very large. The only relatively large effect happens at rating scores group 5, as sellers try to move out of this rating scores group. Nevertheless, even from the limited evidence, the results are still consistent to the rating scores dynamics story. 3.6 Model Extension Competitive Sellers In the basic model used for estimation, seller’s pricing decision only depends on his own rating scores and market conditions such as average prices. The market conditions are given 54 Table 3.7: Model Fits Canon 500d Canon 550d Canon 600d Price Prediction diff (%) Price Prediction diff (%) Price Prediction diff (%) 3.6873 3.6628 0.663 4.2868 4.2811 0.133 4.6270 4.5818 0.977 3.5693 3.6096 -1.129 4.1648 4.2318 -1.610 4.5118 4.5385 -0.591 3.5723 3.5564 0.447 4.1871 4.1826 0.109 4.4851 4.4952 -0.224 3.4048 3.5032 -2.888 4.0634 4.1334 -1.723 4.3862 4.4519 -1.497 3.4027 3.4500 -1.389 4.0937 4.0841 0.234 4.3995 4.4086 -0.206 3.3729 3.3968 -0.708 4.0952 4.0349 1.472 4.4115 4.3653 1.046 3.3390 3.3436 -0.140 4.0254 3.9858 0.985 4.4082 4.3221 1.955 3.3439 3.2905 1.596 4.0314 3.9366 2.351 4.3751 4.2788 2.200 3.2219 3.2376 -0.488 3.9564 3.8874 1.744 4.2958 4.2356 1.402 3.1514 3.1851 -1.069 3.8048 3.8383 -0.879 4.2296 4.1923 0.881 3.0901 3.1329 -1.384 3.7645 3.7892 -0.656 4.1980 4.1491 1.164 3.0701 3.0809 -0.349 3.7015 3.7400 -1.040 4.0692 4.1059 -0.903 55 exogeneously in his decisions. In particular, seller acts as a single agent and do not directly consider the effect of his own prices to other competitors or to the market condition. The model also resembles the assumption of seller’s information about other competitors. It is normally impossible to think of sellers as keeping updated on the evolution of rating scores of each of all competitors and adjusting his pricing accordingly. In the competitive environment like online platform, the assumption of small sellers seems reasonable. Since the competition among sellers are not directly treated, the basic model cannot say too much on the effect of competition. In the model extension, I extend the model to allow competition more directly. In the competitive model, the demand depends on prices of all sellers explicitly. The setting creates a tension as the dimension of market state space is too large to solve the MPE when number of sellers are large. Besides, it is intellectually challenging for sellers to keep tracking the rating scores and the transition of rating scores of each competitors when they make pricing decisions. As will see below, I employed the concept of oblivious equilibrium to solve the problem. The basic settings remain the same: there is a fixed number of n sellers on the platform. Each seller has a rating score displayed on seller’s introductory page, and seller with higher scores is perceived to be better quality. The score for seller j at time t is x jt , where x jt belongs to a discrete, finite setfx 1 ;:::;x K g. On the market, let number of sellers in rating score group x k be s kt 2N , then the vector s t =fs 1t; :::s kt; :::;s Kt g2 S N K captures the rating score distribution on the platform. To simplify calculation, I relax s t as S R K . By definition, å k s kt = n. At each time period t, one unit mass of consumers come and choose to buy one product from one of the sellers. Consumers believe seller with higher rating scores is of high quality 56 on average, so are willing to pay a premium for high rating scores. 10 Concretely, the utility of a consumer from seller j’s product is 11 u jt =g p p jt + å k g sk 1(x jt = x k )+e jt whereg p is the willingness to pay, andg s =fg sk g k is the premium for rating scores. The utility from not purchasing at all is u 0t =e 0t . Lete jt follows an independent, extreme value distribution, then the demand for seller j is d jt = exp(g p p jt +å k g sk 1(x jt = x k )) 1+å j 0 exp(g p p j 0 t +å k g sk 1(x j 0 t = x k )) Contemporaneous profit for the seller isp jt =(p jt c)d jt . Moreover, for each unit of sales realized, sellers receive a feedback from this traction. The update potentially enables the seller to be in a favored rating scores group (if the feedback is good enough) or a less favored group (if the feedback is bad enough). Concretely, the rating score evolves as x jt+1 j(x it ;d jt )= 8 > > > > > < > > > > > : x jt + 1 a 1k + b 1k d jt x jt with prob 1(a 1k + b 1k d jt )(a 2k + b 2k d jt ) x jt 1 a 2k + b 2k d jt (3.8) Sellers on the platform set prices to maximize profit. The problem is dynamic as prices determine both current period profit as well as future profits through rating score updating. The price decision is stationary: seller’s decision is based on its own state x and market state s (i.e. the distribution of sellers rating scores), but not on the time point when the decision 10 In the next sub-section, I provide a rational explanation for the rating score premium. 11 To simplify discussion, I omit the other market condition variables. 57 is made. I restrict seller’s pricing strategy to be symmetric. Let the optimal price for seller at rating score level x k be p k (s). By the symmetry of pricing, the expectation of market state updates as E(s t+1 = s k js t )= s kt [1(a 1k + b 1k d jt )(a 2k + b 2k d jt )] + s k+1t (a 2k + b 2k d jt )+ s k1t (a 1k + b 1k d jt ) (3.9) from the accumulation rule. Suppose seller j with rating score level x k on market with market state s sets prices p(x k ;s), then his value function is v(x;s)=(p(x k ;s) c) d(x k ;s)+dE x 0 ;s 0(V(x 0 ;s 0 )) (3.10) where d(x k ;s)= exp(g p p(x k ;s)+g sk x k ) 1+å k 0 exp(g p p k 0(s)+g sk 0x k 0)s k 0+d(p(x k ); p k ) d(p(x k ); p k ) = exp(g p p(x k ;s)+g sk x k ) exp(g p p k (s)+g sk x k ) is the deviation from setting prices away from the optimal. The solution requires p(x k ;s)= p k (s);8k2 x 1 ;:::;x K ;s2 S, and V(x;s)= argmaxv(x;s) =(p k (s) c) exp(g p p k (s)+g sk x k ) 1+å k exp(g p p k (s)+g sk x k )s k +dE x 0 ;s 0(V(x 0 ;s 0 )) (3.11) The price and value function define a Markov Perfect Equilibrium. Definition. A Markov Perfect Equilibrium is value function V(x;s) and policy function p(x;s) such that: 1. policy function p(x;s) solves the seller’s problem defined in (3.10); 2. value function V(x;s) is defined by (3.11), for any state (x,s); 58 3. the transition of the individual state x is defined in (3.8). However, solving the MPE defined above is a forbidding task due to curse of dimension. For a market with n= 100 sellers and K = 6 possible rating score values, the market state could be any combination of(n 1 : n 6 ) such thatå i n i = 100, which is of hundreds of thousands possibilities. The number of possible market state grows exponentially with K and n. Even I consider a symmetric pricing strategy, tracking the transition of market state Pr(s 0 js) is still impossible. To deal with the high dimension of market state, I follow the work of Weinstraub et al. (2008) to define an oblivious equilibrium (OE). In an oblivious equilibrium, sellers do not pin their decisions on every market state, but rather a long run average. It is a good approximation of the MPE as the change of rating scores for many sellers cancels out so the average is relatively stable. From a behavioral point of view, sellers make near optimal pricing decisions by focusing on average of state distributions, as tracking rating scores and sales of each competitor is too informational costly. Seller j makes his decision depending on his own rating score x jt = x k and long run market state ¯ s. Denote p k for p k ( ¯ s). Notice pricing decision merely depends on the seller’s own rating score, so rating scores evolve as an independent transient Markov chain. By pinning on an expectation of market state, seller determines prices by using information of his own rating scores x k and only needs to adjust pricing when his rating scores change. In this case, seller j’s problem could be written as: ˜ v(x; ¯ s)=(p(x k ) c) ˜ d(x k ; ¯ s)+dE x 0( ˜ V(x 0 ; ¯ s)) (3.12) where ˜ d(x k ; ¯ s)= exp(g p p(x k )+g sk x k ) 1+å k 0 exp(g p ˜ p k 0+g sk 0x k 0) ¯ s k 0+d(p(x k ); p k ) andd(p(x k ); p k )= exp(g p p(x k )+g sk x k ) exp(g p ˜ p k +g sk x k ) is the deviation. By examining the “steady state” condition, the policy function and the associated value function do not depend on the market states but rather on the long run “steady states” ¯ s. I 59 denotef ˜ V; ˜ p; ˜ dg as the steady state equilibrium outcome. I define an oblivious equilibrium such that: Definition. Oblivious Equilibrium f ˜ V; ˜ pg is the value function and policy function for an oblivious equilibrium such that: 1. ˜ p is the solution to (3.12); 2. ˜ V = argmax ˜ v(x) =( ˜ p(x k ) c) ˜ d(x k ; ¯ s)+dE x 0( ˜ V(x 0 )) =(p(x k ) c) exp(g p ˜ p(x k )+g sk x k ) 1+å k 0 exp(g p ˜ p k 0+g sk 0x k 0) ¯ s k 0 +dE x 0( ˜ V(x 0 )) 3. ¯ s is the invariant distribution associated with the transition matrix defined at the price level ˜ p and associated demand ˜ d x jt+1 j(x jt = x k )= 8 > > > > > < > > > > > : x k+1 a 1k + b 1k ˜ d x with prob 1(a 1k + b 1k ˜ d)(a 2k + b 2k ˜ d) x k1 a 2k + b 2k ˜ d Compared with the MPE, the OE does not have the curse of dimension problem. By examining the conditions at steady state, the pricing and value function are not a function of the current market state distribution, but only a function of individual state. The dimension of individual state is much smaller, so the problem is reduced to a much reduced dynamic pro- gramming problem with an additional constraints of invariant distribution for ¯ s. A byproduct benefit of examining only the long run steady state is that the results are more robust. In OE, the transition of state is ignored, so the initial distribution of market state does not affect 60 the results, as long as it leads to the same invariant distribution. The condition is not bind- ing, as the invariant distribution depends only on transition matrix, which itself depends on pricing. Meanwhile, the pricing depends on the invariant distribution, rather than the initial distribution of rating scores. The calculation to solve an OE is equivalent to that of a dynamic programming with a embedded fixed point of market state distribution. The problem can be solved numerically as a embedded fixed point with two loops. In the inner loop, for a given state s (t) I use the conventional value function iteration to getf ˜ p (t) ; ˜ V (t) g. After having solved the pricing f ˜ p (t) g, I calculate the transitional matrix associated and update the invariant state to s (t+1) . The procedure is iterated until s converges. The rating scores-price relationship is very similar to the one in the single agent model. The relationship is illuminated in Figure 3.9 . Both the static prices and dynamic prices increase as rating score is higher, but the dynamic prices are always lower than the static prices due to the rating scores dynamics. Depending on rating scores, the dynamic prices is .5 - 3.5% lower than that of static prices. In this exercise, I can compare the effect of having more competitors on the market more explicitly. Table 3.8 lists the optimal prices and price differences when where are 10, 20 and 30 sellers on the market for one unit of demand. For example, for a seller of rating score in the lowest rating scores group, the price is 3% less than the static pricing when number of sellers is 10, and the discount drops to 1.5% and 1% respectively when the number of sellers increases to 20 and 30 respectively. As number of sellers increases, both the static prices and the dynamic prices decline. The dynamic prices decline even faster. As number of sellers increases, demand is diluted. Each seller has to cut prices even more to gain more sales, so he has less incentive to manage his rating scores by underpricing. As a result, he sets prices less aggressively. 61 Figure 3.9: Prices Comparison Table 3.8: The Effect of Number of Sellers on Pricing N=10 N=20 N=30 price_dynamic price_static price_dynamic price_static price_dynamic price_static 1.004 1.035 1.002 1.017 1.001 1.011 1.039 1.080 1.018 1.038 1.012 1.025 1.127 1.150 1.061 1.073 1.041 1.048 1.185 1.252 1.085 1.123 1.055 1.082 1.344 1.391 1.168 1.196 1.110 1.130 1.548 1.566 1.288 1.295 1.194 1.198 Difference (%) Difference (%) Difference (%) 2.990 1.503 0.999 3.782 1.984 1.335 1.989 1.032 0.688 5.379 3.411 2.438 3.343 2.371 1.783 1.138 0.471 0.259 62 Model Extension: Sellers of two types In the above discussion, I assume an exogeneously given rating scores premium in the demand. As the sellers are homogeneous in their intrinsic quality, the source of such pre- mium seems unclear. Though the homogeneity assumption makes the discussion of dynamic pricing much easier, it cannot explain the existence of the premium in the first place. In this part, I aim to fix this pitfall. I extend the model to allow sellers’ heterogeneity in intrinsic quality. Sellers are of quality type H;L. The probability to achieve higher rating score level is higher for H type than for L type, so the conditional probability of being H type (condi- tional on rating scores) is different from unconditional ones, thus the rating scores are a valid indicator for better quality. Below, I restate the MPE and OE in the context of sellers of two types. At time t, let the market state distribution for type t2fH;Lg be s t t =fs t 1t ;:::;s t Kt g and the fraction of H type be q t =fq 1t ;:::;q Kt g. The observed market state distribution is s t = s H t + s L t : Consumers cannot learn the seller’s type besides the signal of rating scores. The beliefs on q t is updated on information from prior beliefs and transaction history. In this case, the demand for a seller j whose rating score is x k is d jt = exp(g p p jt +g s q kt ) 1+å j 0 exp(g p p j 0 t +å k g s q kt 1(x j 0 t = x k )) That is, consumers are more likely to buy from whom is believed as H type sellers. The only difference from previous model is to replaceå k g sk 1(x jt = x k ) by g s q kt where q kt = g(x kt ) is the fraction of H type conditional on rating score x k . Theng s has an economic meaning as measures of consumers’ willingness to pay for better quality. 63 Sellers of different types are observably equivalent, but have different chance of moving up to a more favored rating score group for the same volume of realized sales. Concretely, the translation matrix for sellers of typet, conditional on realized sales, is x jt+1 j(x it ;d jt )= 8 > > > > > < > > > > > : x jt + 1 a 1k + b t 1k d jt x jt with prob 1(a 1k + b t 1k d jt )(a 2k + b 2k d jt ) x jt 1 a 2k + b 2k d jt (3.13) We assume b H 1k b L 1k for any rating scores level k. When the two are equal, then there is no way to tell the two, and the model degenerates to the model with no seller heterogeneity. The larger the difference of b H 1k and b L 1k , the more likely H type seller can distinguish himself from L type, so H type sellers have a larger incentive to do so. To keep notations simple, I let l t k+ , l t k0 and l t k to denote the probability of rating scores moving up, remaining, and moving down. Given the individual state transition matrix, we can write the expectation of market state transition as (s t+1 = s k js t )=[l H k0 q kt +l L k0 (1 q kt )]s kt (3.14) +[l H k q kt +l L k (1 q kt )]s k+1t +[l H k+ q kt +l L k0+ (1 q kt )]s k1t Consumers update their beliefs on sellers’ quality by Bayesian rule: q k;t+1 =[l H k0 q kt s kt +l H k q kt s k+1t +l H k+ q kt s k1t ] =f[l H k0 q kt +l L k0 (1 q kt )]s kt +[l H k q kt +l L k (1 q kt )]s k+1t (3.15) +[l H k+ q kt +l L k0+ (1 q kt )]s k1t g 64 the expectation of beliefs on sellers’ quality is governed by a mix of the fraction of high type sellers who: 1) remain in the same rating scores group; 2) have moved up from lower rating scores group; 3) have moved down from higher rating scores group. Recall that High type sellers have a higher probability of moving up, the separation is possible: sellers who remained in the same group level are more likely to be Low type sellers, while sellers who moved up are more likely to be High type sellers. As time goes by, the distribution of fraction of High type becomes less concentrated on the low rating scores groups and more concen- trated on the high rating scores groups. Eventually, the separation can be realized to some degree. Given the transition of market state and beliefs on the quality, let the pricing strategy for seller of type t and of rating level x kt at market condition (s t ;q t ) be p t (x kt ;s t ;q t ). Suppose one seller j of typet and of rating level x kt on that same market condition sets price p t jt , then her value function is v t (x kt ;s t ;q t )= d t (p jt ;x kt ;s t ;q t )(p t jt c)+dE[V t (x kt+1 ;s t+1 ;q t+1 )] (3.16) where d t (p jt ;x kt ;s t ;q t )= exp(g p p t jt +g s q kt ) 1+å t2fH;Lg å k exp(g p p t (x kt ;s t ;q t )+g s q kt )s t (x kt ) I define a MPE for two-types sellers as follows: Definition. A Markov Perfect Equilibrium is value function V H (x;s;q) and V L (x;s;q) and policy function p H (x;s;q) and p L (x;s;q) such that 1. value function V t (x;s;q) achieves the optimal value at price p t (x;s;q), as defined by V t (x;s;q)= maxv t (x;s;q) = d t (p t (x;s;q);x;s;q)(p t (x;s;q) c)+dE x 0 ;s 0 ;q 0[V t (x 0 ;s 0 ;q 0 )] 65 2. p t (x;s;q) maximizes the value function V t (x;s;q) defined in (3.16). 3. the state variable and beliefs on quality evolve as defined in (3.13),(3.14) and (3.15). Again, the MPE is not tractable to solve, as the dimension of market state (s;q) is too large. Similar to the basic model, I define an Oblivious Equilibrium as the long term asymp- totic of the Markov Perfect Equilibrium. Let the long run market state for the two types of sellers be ¯ s H and ¯ s L , then the market state is ¯ s= ¯ s H + ¯ s L and the fraction of High type is ¯ q= ¯ s H = ¯ s L . Instead of reacting to the current market state, sellers only take advantage of the long run expectation and make their pricing decisions accordingly. Let the optimal pricing strategy be ˜ p t (x; ¯ s; ¯ q). In this case, the decision depends on seller’s own state, but not on others. Seller j saves himself the trouble of tracking others every period, and adjusts prices only when his own rating scores change. Let the optimal pricing be ˜ p t (x)= ˜ p t (x; ¯ s; ¯ q), then seller j’s problem could be written as: ˜ v t (x k )=(p t (x jt ) c) ˜ d(x k ; ¯ s)+dE x 0( ˜ V(x 0 )) (3.17) where ˜ d(x k ; ¯ s)= exp(g p p t (x jt )+g sk ¯ q k ) 1+å t2fH;Lg å k exp(g p ˜ p t (x k )+g s ¯ q kt ) ¯ s t (x k ) By examining the “steady state” condition, the policy function and the associated value function do not depend on the market state but rather the long run state ¯ s. I denotef ˜ V t ; ˜ p t ; ˜ d t g as the steady state equilibrium outcome. I define an oblivious equilibrium as: Definition. An oblivious equilibrium is value function f ˜ V H ; ˜ V L g and pricing decision f ˜ p H ; ˜ p L gsuch that 1. value function ˜ V t (x; ¯ s; ¯ q) achieves the optimal value at price ˜ p t (x; ¯ s; ¯ q), as defined by ˜ V t (x; ¯ s; ¯ q)= ˜ d t ( ˜ p t (x; ¯ s; ¯ q);x; ¯ s; ¯ q)( ˜ p t (x; ¯ s; ¯ q) c)+dE x 0[ ˜ V t (x 0 ; ¯ s; ¯ q)] 2. ˜ p t (x; ¯ s; ¯ q) maximizes the value function ˜ V t (x; ¯ s; ¯ q); 66 3. ¯ s t is the invariant distribution associated with the transition matrix defined at the price level ˜ p t and associated demand ˜ d t ; 4. ¯ q= ¯ s H =( ¯ s H + ¯ s L ). The OE is calculated by a similar algorithm as used for basic model. The only complex comes from the evaluation of quality, as the fraction of High types is endogenously deter- mined in the two type model. Nevertheless, a similar embedded fixed point algorithm is applicable to solve the OE. I provide an example to illuminate the equilibrium. In the example, I assume half of the sellers are of High type and the other half are of Low type, and all sellers locate in the lowest rating scores group initially. For same amount of realized sales, the probability of rating scores moving up for High type is twice as large as that for Low type. Consequently, High type sellers have higher incentive to manage their rating scores. In equilibrium, the prices of High type is lower than that of Low type. The prices are illuminated in Figure 3.10. The prices for High type is always lower than that for Low type, and both prices are lower than the static prices. By the chosen parameters, the discount is small: High type seller’s price is .1% lower than the static prices, and Low type seller’s price is .03% lower. The existence of rating scores system separates the two types, at least partially in the long run. Table 3.9 lists the ratio of High type for each rating scores level in equilibrium. In the long run, around 38% of sellers in the rating scores group 1 is High type sellers, and that fraction is 52% for the rating scores group 6. I have illuminated a case where the existence of rating scores are informative even when the price difference is mild. Table 3.9: Asymptotic Distribution 1 2 3 4 5 6 38.473 40.374 42.265 43.337 45.960 52.815 % number stands for fraction of sellers of High type in each rating scores group 67 Figure 3.10: Prices Comparison for two types 3.7 Discussion Rating scores help sellers to attract demand and achieve higher profits, and sellers should pay attention to manage the rating scores. Using a unique identification condition on Taobao, I find evidence that sellers do have rating scores dynamics concerns. I show in an environment where rating scores accumulation depends on both ratings per transaction and transaction volumes, sellers undercut prices to attract more sales and reviews to accelerate rating scores accumulation. Estimation results suggest sellers’ management of rating scores even when the rating scores premium is not very significant. I also show that the effect does not depend on the single agent decision setting. In a competitive setting, sellers still have such rating scores dynamics concern, though the effect is affected by competition from competitors more explicitly. Last, I show the rating score system is informative: it can separate sellers of different types and help consumers to choose sellers. 68 The model can be further extended in the following directions. First, I can allow sellers to choose the effort of service, and the effort level affects the accumulation of rating scores. That is, I can add moral hazard into the model and check whether the rating score system is still informative or not. In some studies such as (Mailath and Samuelson, 2001), it is found that sellers may accumulate reputation and milk it when it is at high levels. If it also happens in my environment, then it is likely that the rating scores system becomes not informative. Second, I can allow sellers to sell two products of different marginal cost. Sellers can use one product as the main source for rating scores accumulation and the other as the main source for profits. Restricting seller’s decision on one product potentially over states the cost of managing the rating scores. Third, I can add entry and exit decision into the model, to make the fraction of High type sellers in the long run to be endogenous. From the estimation side, due to the lack of information on the demand side, I have to restrict demand model to a simplified and aggregated form. The demand can be more random, heavily affected by other factors such as seller’s advertising. Since such information is missing in the estimation, it is possible to confuse the effect of rating scores and advertising. It is possible that advertising leads to both increase of rating scores and large trade volumes, but the effect is not detected in the data. Part of the concerns discussed here can be addressed by my ongoing project. I am looking at a platform to link IT service providers and the firms outsourcing the service. I allow service providers to choose the scope of their services as well as managing their rating scores. I can allow service providers to accumulate rating scores on easy jobs, and use the high ratings to compete for more complicated jobs. The possible service choices are limited so the model is feasible. Advertising on that platform is also limited, so it is a less concern. 69 Chapter 4 Display Order and Consumer Search of Asymmetric Products (joint with Lin Liu) abstract The conventional wisdom on online shopping intermediaries (e.g. Alibaba’s Taobao Mall or Yahoo!Shopping) presumes that they help consumers to learn useful product information and find desirable products with reduced search efforts. However, evidence suggests that some- times intermediaries steer consumers’ attention toward the products that provide lower fits. An important feature of shopping intermediary is that it hosts third-party sellers and charges them a percentage of the final revenue as a commission fee. Capturing this feature, we pro- vide an equilibrium model of an intermediary, sellers and consumers and we explore several important managerial questions: when does the intermediary direct consumers’ attention to good fitting products and when does not? How do the features of products (e.g. fitness) affect intermediary’s selection of the display order? How does the display order affect con- sumer search and sellers’ price competition? Our results suggest that the intermediary selects descending display order (good fitting product displayed first) when search costs are suffi- ciently high. Otherwise, the intermediary selects ascending display order (less fitting product displayed first). In addition, we also show how market parameters (e.g. product fit probabili- ties) affect intermediary’s consideration in product display order selection. 70 4.1 introduction With the explosive growth of the Internet, various online shopping intermediaries, like Alibaba’s Taobao Mall or Yahoo!Shopping, have been created to link sellers and consumers. These sellers are mostly independent from the intermediaries and often provide various prod- ucts with different features, qualities or popularity to consumers. Consumers seek and eval- uate product information to find their desirable ones from the thousands of available alterna- tives. It is well known that information presentation format affects consumers’ information acquisition patterns (Bettman and Kakkar, 1977). Specifically, experimental evidence shows that in an online environment consumers’ attention and product evaluation process follow top-down and left-right manners. This renders significant prominence to the products that are displayed on the top of a search result compared to the ones that are listed down in the result. And data suggests that consumers’ attention and click-through rates of the first alternative can be 17 times higher than those of the eighth alternative (Pan et al., 2004). Built off on this knowledge, online shopping intermediaries create a search environment to influence consumers’ information acquisition process. For instance, shopping intermedi- aries often keep track of the popularity of the available products based on sales. When con- sumers search products in an intermediary’s search engine without applying specific sorting rules (e.g. price from low to high), shopping intermediaries generate a default search results to consumers based on the popularity (see Figure 1). According to a manager of Taobao Mall, the default search results are very important in search environment design. Specifically, the product display order in these search results can be used to steer consumer’s attention towards some specific products. Much thought has focused in which products should be displayed on the top of these search results because it is found that about half of the consumers use these search results in their product evaluation and most of them start their evaluation from those prominent spots. 71 The conventional wisdom on shopping intermediaries presumes that platforms design a search environment to help consumers to find the desirable product with reduced search costs ((Spulber, 2006)). Many people believe that the products that potentially fit most consumers’ tastes are expected to be displayed on the top in the search results because in this way a consumer can easily find the potentially desirable product in her mind. However, evidence suggests that sometimes intermediaries are found to do the opposite on purpose. Specifically, they may divert consumers’ attention toward some products that do not meet a wide range of consumers’ tastes by displaying them on the top of the search results 1 . In this paper, we explore an intermediary’s incentive in the selection of product display order in the default search result and we provide a potential explanation to why sometimes a shopping interme- diary does not want to help consumers to easily find the products that might be potentially more desirable to them. To answer this question, it is important to understand several important features of online shopping intermediaries. First, the common feature of online shopping intermediaries is that they host third-party sellers and typically charge a percentage of the final transaction price as a commission fee. In addition, unlike conventional retailers, the intermediary allows sellers to set prices of their products. This revenue sharing scheme implies that intermediary has an incentive to keep sellers’ competition in check. Consequently, an intermediary needs to maintain sellers’ profits besides helping consumer to search. Intuitively, this should rein- force the conventional wisdom about the supportive role of the online shopping intermedi- aries because by displaying first the products that are more likely to meet consumers’ needs they will search less and sellers can charge higher prices. However, what is missing from this argument is the competitive interactions between the asymmetric sellers. In this paper, we explore this competitive interactions and study an important managerial question: How should an online shopping intermediary design the product display order to help consumer search while ensuring the profitability of its hosted sellers? 1 Wall Street Journal, November, 2007, “Where, E-Commerce Meets Chat, Social Retailing Gains Traction”. 72 In addition, most of the time, the price information is more transparent in the search environment of an online shopping intermediary than the product fit information. Thus, it is easier for consumers to inspect prices than evaluate product fit. For example, figure 1 illustrates a snapshot of laptops available on Alibaba’s Taobao Mall. One can observe that the laptops’ prices are transparent and highlighted to consumers but the laptops’ fit information is very brief. To obtain detailed information about product fit, consumers have to click into a specific model and read product description in more details. This implies that when using the search results to evaluate products consumers might need to spend more time and effort in acquiring fit information than obtaining price information, Thus, to capture this feature, we focus on consumers’ product fit evaluation and use search cost associated with learning product fit as the focal variable in our discussion. Our findings show that this search cost plays a key role in determining shopping intermediary’s product display orders. The first new insight regards intermediary’s selection of product display order. We show that there is a threshold search cost which determines the product display order selected by the intermediary. Specifically, when search costs are smaller than this threshold, the intermediary may not want to first display the product that is more likely to fit consumers’ tastes (denoted as high potential product afterwards). Specifically, with small search costs, consumers are more likely to search the second product down in the recommended list. Under this situation, if the low potential seller is displayed in the second spot, he may actively lower his price to attract and retain consumers. This puts downward pressure on the high potential seller (displayed in the first spot) and forces him to lower his price. Due to the revenue sharing scheme, the intensified competition between sellers also lowers intermediary’s profit. Thus, the intermediary should first display the low potential product in the recommended list. This challenges the conventional wisdom about the supportive role of intermediaries to consumers. Alternatively, with relatively large search costs, consumers are less likely to search the second product. Thus, even when the low potential seller is displayed in the second spot, he may no longer want to aggressively lower his prices to induce consumers search. Instead, he wants to 73 select a high price to better exploit the consumers who happen to prefer his product, implying softened price competition between sellers. Thus, the intermediary should first display the high potential product when search costs are sufficiently high. The second new insight concerns the properties of the threshold search costs with regards to products’ fit probabilities. Specifically, our findings show that the threshold search costs increases in fit probability of the high potential product. That is, the intermediary tends to select ascending product display order (low potential product displayed first) when the fit probability of high potential product increases. As this fit probability increases, the market segment that only likes the high potential product expands and the market segment that only likes the low potential one shrinks. Thus, in the ascending order, the high potential one is more willing to maintain high prices to exploit this market segment than the low potential one in the descending order. This softens price competition between the two products and also benefits the intermediary. In contrast, our findings also show that the threshold search costs first increase and then decrease in the fit probability of the low potential product. Equivalently, the intermediary tends to first select ascending order and then select descending order when that of low poten- tial product increases. This key difference is driven by the strong incentive of the low poten- tial product’s to set low prices to induce consumers to search. Specifically, when the fit prob- ability of the low potential product is small and increases, if displayed in the second spot (or equivalently if the descending order is selected), the seller of the low potential product wants to set low prices to attract consumer search and this intensifies price competition, implying that the intermediary’s profit decreases. However, as his fit probability continue increasing and become more and more closer to that of the high potential product, our findings show that if displayed in the second spot the seller of the low potential product has less incentive to set aggressive prices to lure consumer search. Rather, he becomes more like the seller of the high potential product and wants to maintain high prices to exploit the market segment that 74 only likes the realized value of the low potential product. This implies that the intermediary’s profit no longer decreases as the fit probability of the low potential product increases. Our work is related to the literature on online shopping intermediaries with consumers and sellers (Chen et al., 2002; Iyer and Pazgal, 2003). Both studies, however, focused on situations in which consumers know the specific product they want to buy and use the inter- mediary to find the best price. In contrast, there is another major role of the intermediaries as disseminators of non-price information (Iyer and Padmanabhan, 2006), which is the focus of our paper. Specifically, we study the situation in which a consumer uses the intermediary to find the desirable product based on non-price attributes and this product evaluation pro- cess is a function of the intermediary’s selection of product display order. This requires the intermediary to integrate consumer’s optimal search behavior into its choice of display order. In addition, the marketing and economics literature has recognized that the online plat- forms play a key role in making consumers find their desirable products with reduced search costs (Spulber, 2006; Häubl and Trifts, 2000). However, this is not always the case. Liu and Dukes (2014) showed that the optimal search environment should embeds sufficient search costs to prevent consumers from searching too many sellers but not too much to prevent eval- uating too few product attributes. However, they studies how online platforms designs search environment facing symmetric sellers. In contrast, we focus the situation where the interme- diary needs to consider the display order of asymmetric products and we identify the profit maximizing display order for the intermediary. Roth and Sotomayor (1992) have studied the market design of matching mechanism and derived efficiency from a social planner’s perspective. In contrast, Hagiu and Jullien (2011) explored matching mechanism design by a profit-maximizing platform (e.g. Google Shop- ping) which collects revenue through pay-per-click (PPC) from sellers. Specifically, the plat- form’s profit in their paper depends on the number of clicks by consumers, implying that the platform has an incentive to encourage more clicks. However, the intermediary (e.g. Alibaba’s Taobao Mall or Yahoo!Shopping) in our study is different and it adopts revenue 75 sharing scheme through commission fees. This key difference requires new insights for the intermediary’s matching mechanism design. Our work is also related to the growing literature of prominence and consumer search. Armstrong et al. (2009) studied the situation in which consumers’ search order is pre- determined by the products’ display order and they focus on symmetric firms. In contrast, we study asymmetric firms and we show that this alters consumers’ incentive in their search behavior which the intermediary wants to consider in designing its search environment. The consumer search literature has been focused on the competitive interactions between firms (Wolinsky, 1986; Anderson and Renault, 1999). The conventional results suggest that firms’ competition is softened when consumers find their most desirable products without intensive search across firms. However, with asymmetric products, we show that sometimes letting consumers find their most preferred product more easily might not necessarily create higher market power for firms, which the intermediary has an incentive to keep in check. 4.2 Model There is an online shopping intermediary. For simplicity, we assume that there are two sellers on the intermediary. Each seller provides one product and chooses the price of his product. The products are different in their popularity, which is operationalized as the potential to provide a good fit to consumers. We use H to denote the high potential seller’s product (H product) and L to denote the low potential one (L product). Denote a i the probability for consumers to obtain a good fit from the product i, thena H >a L , i.e. H product has a better chance to fit consumers’ taste. The fit probability a i reflects that the range of such tastes product i can satisfy. Specifically, highera i reflects that product i can cater to a wider range of tastes or more popular to most consumers. For example, a mass market brands may meet a wider range of consumers’ tastes than a designer brand. Thus, a mass market product is more 76 popular to an average consumer than a designer one. We assume that the realized fit of the two products are independent from each other. The mass of the consumers is normalized to one and each consumer has a unit demand. Consumers initially have imperfect information about the realized fit of the products before evaluation but they know the distributions of fit which are different across these two sellers’ products. In addition, they can uncover the realized fit of the products through costly evalu- ation. Specifically, for simplicity, we let the consumer learn the fit of the top product in the search result for free but incur a search costt (t 0) to learn the second one. 2 In addition, we assume that consumers only search for product fit and they observe prices of both prod- ucts. This assumption is contingent on the important feature of an intermediary that price information is significantly more transparent and easy to observe than the fit information in the search environment. And the previous literature has focused on intermediary’s role as disseminators of price information. Abstracting from this issue in this study, we focus on intermediary’s role in providing non-price information and restrict our attention to consumer search on fit information. Consumer’s utility of product i= H=L is given by u i = v i p i where v i is the consumer’s value from consuming product i and p i is the price of seller i’s product. For simplicity, we assume that the consumer always obtains zero value from a bad fit (v i = 0). A good fit provides positive value to the consumer, v i > 0. We assume that this value is a random draw from a uniform distribution [0;1] and is the same for both products. 3 That is, two products provide the same level of satisfaction to consumers if they 2 Other studies of ordered search (e.g.(Gu and Liu, 2013)) also adopt the same assumption about search costs for the purpose of tractability. 3 The similar setting can be also seen in other search models ((Chen and He, 2011); (Athey and Ellison, 2009)). 77 both fit consumers’ tastes. The value of the realized fit is private information to the consumer reflecting consumers’ idiosyncratic tastes. We normalize the outside option of not buying to be zero. Obviously, the consumer does not buy when she finds bad fit from both products. However, if she evaluates both products and finds good fit from both of them, she selects the cheaper one. And we refer this type of consumers as switchers. Alternatively, if only one product provides good fit, she selects it conditional on that the utility of this product is positive. We refer this latter type of consumers as non-switchers. The intermediary selects the display order of the two products. We consider two different orders: descending order and ascending order. Specifically, H product is displayed first in the descending order while L product is displayed first in the ascending order. According to a manager of Alibaba’s Taobao Mall, product display orders of the default search result reflect relatively stable product features (e.g. the potential to fit consumers’ taste) and are updated weekly. Display orders do not reflect instant prices unless consumers apply specific sorting rules contingent on prices (e.g. prices from low to high) in the search process. In addition, evidence from a recent WSJ article shows that on average sellers change prices in an hour- by-hour manner on shopping intermediaries. This implies the following timing of the model: first, the intermediary chooses the product display order. Specifically, it can either first display the high potential product followed by the low one, or alternatively, first display the low potential one followed by the high one. Second, two sellers set their prices simultaneously with the knowledge of the display order. Third, consumers sequentially evaluate the products and buy the more desirable one, or do not buy anything and leave the market. As a starting point, we begin with a benchmark case with zero search costs. In this case, the consumer has perfect information about the products’ fit, implying that the display orders of products do not make any difference to the sellers and the intermediary. Then, we explore the case with non-neglected search cost and we compare the results to those in the benchmark case. Specifically, we show that, with non-neglected search cost, the display orders create significant difference in affecting sellers’ competition and consumer search, implying that a 78 strategic shopping intermediary can select its optimal display order to keep the competition in check. 4.2.1 Benchmark: Zero Search Costs When the search cost is zero (t = 0), the consumer costlessly learns the fit of both products. Under this situation, her product selection has three cases: (1). if only one product fits her tastes, she selects that product; (2). if no products provide good fit, she does not buy anything and leaves the market; (3). if both fit her tastes, she selects the cheaper one. The market is thus divided into four segments, and we summarize the market size in Table 1. p H p L p H < p L d H (1a L )a H a H d L a L (1a H )a L Table 1: Market Sizes (d H and d L respectively denotes the market size for product H and L) The market size in Table 1 does not reflect the actual consumer demand because the consumer buys a product only when its value exceeds its price. Thus, given any price p i , the actual consumer demand is d i (1 p i ). This implies that the profit for product i is p i = d i p i (1 p i ): Let ˜ p(p i ) p i (1 p i ) be the profit from one unit of product i, which only depends its own price but not the price of his competitor. We show the sellers adopt a mixed pricing strategy and the results are summarized in the following lemma. Lemma 1. With zero search costs, sellers adopt a mixed pricing strategy and p H first order stochastically dominates p L . (i). H product sets price p H 2( 1 p a L 2 ; 1 2 ) with probability 1b with unconditional cdf F H (p)= 1 a H ˜ p(p) ˜ p( 1 p a L 2 ) ˜ p(p) and sets price at 1 2 with probability b, where b = 1 a L a H . The expected profit for H product isa H (1a L )=4; (ii). L product sets price p L 2( 1 p a L 2 ; 1 2 ) and its cdf is F L (p)= 1 a L ˜ p(p) ˜ p( 1 p a L 2 ) ˜ p(p) . The expected profit for L product isa L (1a L )=4. 79 (iii). The expected profit of H product is higher than that of L product. This lemma illustrates an intuitive result that on average the price of L product is lower than that of H product. Both sellers would like to lower their prices to attract switchers. However, both sellers do not want to set their prices too low to avoid losing potential profit from their non-switchers. Consequently, both sellers randomize their prices to sometimes compete for switchers and sometimes extract surplus from the non-switchers. Seller H is less willing to cut his prices in this competition because he has a larger fraction of non-switchers. This implies that the expected price of H product is higher than that of L product. As a result, the expected profit of H product is also higher. It is noteworthy that the two sellers have the same lowest prices. Consumers buy a product either because it is the only one which provides a good fit or because it is cheaper than the rival product which also provides a good fit. The former encourages sellers maintaining high prices while the latter forces them to set competitive prices. And with zero search costs, it is never beneficial for a seller to set prices lower than the lowest price of the rival product because doing so this seller can not obtain more demand. However, this is not true with non- neglect search costs. Specifically, when evaluating products is no longer free to the consumer but prices are transparent, a seller which is not evaluated can strategically lower its price to induce the consumer to search his product. As we will see below, the lowest prices of the products is different from the wedge of the search cost. Because the search cost is zero, the consumer has perfect information about products. This implies that the product display orders play no rule in affecting the consumer’s product information. Thus, the display orders do not affect sellers’ competition, which in turn have no influence on the shopping intermediary’s profit. However, with non-neglected search costs, the fit information of the second product is no longer transparent if the consumer does not evaluate it. This affects sellers’ competition and it is no longer obvious how the display orders affect the shopping intermediary’s profit. In the next two sections, we study how a given display order affects consumer search and sellers’ competition with non-neglect search 80 costs. Then in section 4.2.4 we explore how the shopping intermediary selects its optimal display order. 4.2.2 Descending Display Order In this sub-section, we focus on the descending display order. When the intermediary selects the descending order, both sellers and consumers know that H product is displayed first and Lproduct is displayed in the second spot. The consumer decides whether to incur the search costs to evaluate the second product (L product in this situation), after observing the fit and price of H product. If the consumer evaluates L product, she buys the more desirable one from the two sellers. Otherwise, she buys H product if it is worth doing so. To summarize, if the consumer finds a good fit from H product, she chooses to evaluate L product only when v i p H a L (v i p L )+(1a L )(v i p H )t That is, the consumer goes on inspecting L product only when he believes he can save more if L product provides a good fit. The expression on the left hand side of the inequality represents the utility of H product and the one on the right hand side represents the expected net surplus of evaluating L product given that H product provides a good fit to the consumer. Specifically, the first term on the right hand side represents the expected utility of obtaining a good fit from L product, the second term represents the expected utility of obtaining a bad fit from L product (under this situation, the consumer returns and buys H product), and the third term is the search cost. Equivalently, the above inequality can be reduced to ta L (p H p L ) 81 That is, L product has to set a relatively lower price to induce consumer search when H product provides a good fit. Define function f des such that f des (p L ) p L +t=a L If p H < f des (p L ), the consumer will not evaluate L product if she finds a good fit from H product. Accordingly, the consumer’s demands for H and L product are a H (1 p H ) and (1a H )a L (1 p L ) respectively and the profits area H e p(p H ) and(1a H )a L e p(p L ) respec- tively. Alternatively, if p H f des (p L ), the consumer will evaluate L product even if she finds a good fit from H product because the price of L product is sufficiently attractive to induce her search. After evaluating L product, if she finds a good fit, she will buy L product because it is cheaper. Otherwise, she returns to buy H product because it provides a good fit. Consequently, the consumer’s demands for H and L product are(1a L )a H (1 p H ) and a L (1 p L ) respectively and the profits are(1a L )a H e p(p H ) anda L e p(p L ) respectively. We denote[p i ; p i ] as the price range of product i. Each seller chooses its price to maximize its profit. The following lemma characterizes sellers’ equilibrium prices and expected profits when the intermediary selects descending display order. Lemma 2. In descending display order, sellers choose mixed pricing strategy in equilib- rium.The expected profit of H product is non-decreasing in search costs and the expected profit of L product decreases in search costs when search costs are low and is independent of search costs when they are large. The total profit of the two sellers first decreases, then increases, and eventually is con- stant, as search costs increase. Depending on magnitude of the search cost, the equilibrium is in one of the three situa- tions. situation 1. When search costs are relatively small, sellers choose mixed pricing strategy (details available in Appendix). The expected profits for H and L product are respectively 82 a H (1a L ) ˜ p( ¯ p H ) and[a L (1a H )+ba H a L ] ˜ p( ¯ p L ), whereb is the probability that H prod- uct sets price at ¯ p H ; situation 2. When search costs are modest, sellers choose mixed pricing strategy. The expected profits for H and L product are respectively [a H (1a L )+ga H a L ] ˜ p( ¯ p H ) and a L (1a H ) ˜ p( ¯ p H ), where whereg is the probability that L product sets price at ¯ p L ; situation 3. When search costs are relatively large, the equilibrium prices for H and L product are ¯ p H and ¯ p L respectively and the expected profits are respectively a H ˜ p( ¯ p H ) and a L (1a H ) ˜ p( ¯ p L ). Lemma 2 shows that the expected profit of L product is non-increasing in search costs while that of H product is non-decreasing in search costs. Specifically, when search costs are small (t <t 1 ), it is relatively cheap for switchers to evaluate the second product (L product) in the search result, implying that L seller has a chance to set attractive prices to compete for these consumers. When search costs increase, it is more costly for switchers to search L product. Thus, L seller has to set more attractive price by continuously lowering his price and this lowers his profit. However, although L seller sets more competitive prices as search costs increase, our result shows that the expected profit of H product is not influenced because he can always maintain the profit from his non-switchers. That is, as search costs increase, if L product’s price is fixed, fewer consumers evaluate L product. However, L seller wants to set low prices to compete for consumers. H Product adjusts accordingly to search cost change, but the effect on profits is canceled by L product’s pricing adjustment. When search costs are median (t 1 tt 2 ), further lowering price to compete for switchers is no longer in the interests of L product because of the high search costs. Instead, he wants to keep high prices to better exploit the non-switchers. Thus, his expected profit remains constant. In addition, H seller benefits from the increase of search costs because fewer consumers choose to evaluate L product when they find a good fit from H product. This increases his market power and profit. When search costs are sufficiently high (tt 2 ), consumers do not evaluate L product if they find a good fit from H product, implying that there are no switchers. Under this 83 situation, H product get the demand of all consumers who find H product fit, and L product get the demand of all consumers who find H product does not fit and L product fits. The high search cost grants H product monopoly power, and L product only gets the remaining demand. Thus, as in the situation with median search costs, L seller sets high prices to fully exploit the non-switchers and his profit remains constant. Similarly, the profit of H product is also constant. (please double check the argument of this paragraph. Especially please check consumer search behavior in these three situations and sellers’ corresponding reactions.) 4.2.3 Ascending Display Order We now consider the ascending display order in which L product is displayed first. All the assumptions are similar as in the case of descending display order. In the ascending order, the consumer knows the fit of L product for free and she decides whether to incur search costs to evaluate H product. If she finds a bad fit, she continues to search H product. If she finds a good fit from L product, she chooses to evaluate H product if v i p L a H (v i p H )+(1a H )(v i p L )t which can be reduced to ta H (p L p H ) Again, like in the descending display order, this condition illustrates that the consumer eval- uates H product only when the net benefit of evaluation exceeds the net cost. Define function f as such that f as (p L ) p L t=a H If p H f as (p L ), the consumer will not evaluate H product if she finds a good fit from L product. Accordingly, the consumer’s demands for H and L product area H (1a L )(1 p H ) 84 anda L (1 p L ) respectively and the profits area H (1a L )e p(p H ) anda L e p(p L ) respectively. Alternatively, if p H < f des (p L ), the consumer will evaluate H product even if she finds a good fit from L product because the price of H product is sufficiently attractive to induce her search. After evaluating H product, if she finds a good fit, she will buy H product because it is cheaper. Otherwise, she returns to buy L product. Consequently, the consumer’s demands for H and L product are a H (1 p H ) and a L (1a H )(1 p L ) respectively and their profits are a H e p(p H ) and a L (1a H )e p(p L ) respectively. The following lemma characterizes sell- ers’ equilibrium prices and expected profits when the intermediary selects ascending display order. Lemma 3. In ascending display order, sellers choose mixed pricing strategy in equilibrium. In addition, the expected profit of H product is constant and the expected profit of L product increases in search cost.The total profit of the two sellers first increases and the is independent of search costs, as search costs increase. Depending on the magnitude of search cost, the equilibrium is in one of the situations. situation 1. When search costs are small, sellers choose mixed pricing strategy (details available in Appendix). The expected profits for H and L product are respectively a H (1 a L ) ˜ p( ¯ p H ) and [a L (1a H )+ba H a L ] ˜ p( ¯ p L ),where b is the probability that H product sets price at ¯ p H ; situation 2. When search costs are large, the equilibrium prices are ¯ p H and ¯ p L respec- tively. The expected profits for H and L product are respectively a H (1a L ) ˜ p( ¯ p H ) and a L ˜ p( ¯ p L ). Similar to H product in Lemma 2, the first displayed product, L product, in the ascending display order has non-decreasing profit as search costs increase. Specifically, when search costs are small (t <t 3 ), the consumer may want to evaluate H product but she is less likely to do so as search costs increase. This increases L product’s profit. Seller H chooses randomized prices to balance the surplus obtained from the switchers and non-switchers. As search costs increase, he is more likely to set higher prices to better exploit his non-switchers but this 85 loses switchers. Our result shows that the two sides of this trade-off is canceled out exactly and seller H’s profit remains constant. Alternatively, when search costs are sufficiently high (t >t 3 ), a good fit from L product prevents the consumer from evaluating H product. Thus, both sellers set high prices to fully exploit non-switchers and their profit remain constant. 4.2.4 Display Order Selection From Lemma 2 and 3, we understand how sellers’ competition and consumer search are affected by the display orders. In this section, we investigate the important question: how does the intermediary select the product display order. Denoter(r > 0) as the intermediary’s fixed commission fee. Given a display order, the intermediary’s profit is r[p H (order)+ p L (order)], where order=des or as respectively denotes the descending and ascending display order selected by the intermediary, and p H (order) and p L (order) are respectively H and L product’s profits which can be found in Lemma 2 and 3. The intermediary selects the optimal product display order to maximize its profit and it considers seller’s reaction to the display order on their price decisions and the impact on their profits. Specifically, the intermediary’s selection of product display order is summarized as follows. 8 > > > > > < > > > > > : descending p H (des)+p L (des)>p H (as)+p L (as) indi f f erent i f p H (des)+p L (des)=p H (as)+p L (as) ascending p H (des)+p L (des)<p H (as)+p L (as) The following proposition characterizes the intermediary’s equilibrium choices of product display order. Proposition 1. There exists a unique threshold search costt such that: (i). whent>t ; the intermediary selects descending display order; (ii). when t = t , the intermediary is indifferent between descending and ascending order; (iii). when 0<t <t , the intermediary selects ascending display order. 86 This proposition illustrates that it is not always beneficial for the intermediary to first display H product especially when search costs are small. With small search costs, the con- sumer is more likely to evaluate the second product. If L product is displayed in the second spot, seller L knows that inducing the consumer to evaluate its product is not costly. Thus, he wants to lower the price of his product to attract consumer to search for his product. This puts downward pressure on H product because H seller has to lower his price in order to retain consumers and avoid them from evaluating L product. As a result, both sellers cut their prices and competition is intensified. This is not profitable for the intermediary due to the revenue sharing scheme. Thus, the intermediary does not want to first display H product and then display L product when search costs are small. Instead, the intermediary selects ascending display order by first displaying L product. Alternatively, when search costs are large, our result shows that the intermediary wants to select descending display order by first display H product. With large search costs, the consumer has lower incentive to search the second product, especially if the second product is L product. In addition, if the intermediary displays L product in the second spot, seller L knows that attracting consumers to search its product is difficult due to the large search costs and it is not profitable to compete for switchers by pricing aggressively. Thus, under this situation, seller L wants to charge high price to fully exploit the non-switchers. As a result, seller H can react by maintaining his pricing power and charging high price. The softens competition between sellers incentivizes the intermediary to select descending display order. In addition, similar as L product in Lemma 2, H product in Lemma 3 wants to some- times set low prices to compete for switchers and sometimes set high prices to exploit non- switchers. However, H seller has more non-switchers thus he has lower incentive to reduce price to attract switchers. Thus, compared to the descending display order where L product is displayed as the second product, seller H and seller L compete less aggressively in the ascending display order when search costs are sufficiently low. 87 Proposition 1 illustrates the importance of the threshold search costst in the intermedi- ary’s selection of product display order. However, how the threshold search costs are affected by the products’ fit probability (a H anda L ) is still not straightforward. Next, we explore the property of the threshold search costs with regards toa H anda L .. Proposition 2. (i). the threshold search costt increases ina H ; (ii). the threshold search costt first increases and then decreases ina L . Part (i) of this proposition illustrates that the intermediary tends to select ascending product display order when the fit probability of product H increases. Specifically, as a H increases, the portion of product H’s loyal consumers (a H (1a L )) increases but portion of product L’s loyal consumers (a L (1a H )) shrinks. Thus, if product H is displayed as the second product, or equivalently if the ascending display order is selected, product H is more willing to maintain high prices to exploit its loyal consumers. This softens the price compe- tition between the two products and also benefits the intermediary. However, as illustrated by part (ii) of proposition 2, the intermediary tends to select ascending product display order when the fit probability of product L is low, but tends to select descending display order when it is high. From the arguments of Lemma 2 and3, we know that if displayed as the second product product H is more willing to maintain high prices than product L. And the changes of a L directly affects product L’s incentives if it is displayed as the second product. Specifically, when a L is small, it has more incentive to set low prices to attract consumer search as its fit probability increases. Whena L increases, both the portion of switchers(a L a H ) who find good fits from both products and the portion of loyal consumers of product L(a L (1a H )) increase. The increase in portion of switchers increases product L 0 s incentive to compete for these consumers (by a lower price), and the effect dominates the incentive to exploit the loyal consumer base (by a higher price) whena L is small. And this implies that product H has to react by setting low prices and the competi- tion is intensified. To avoid this, the intermediary tends to select ascending product display order. In contrast, whena L is sufficiently high, if displayed as the second product, product L 88 has stronger incentive to set high prices to exploit its loyal consumers. However, if displayed as the first product, product L might want to set low prices in order to avoid consumers from evaluating product H, which intensifies competition. Thus, the intermediary tends to select descending product display order. Results (i) and (ii) in proposition 2 also show the partial effect of the two different prob- ability of fit is not the same. It indicates the intermediary would have different display order preference when the fitness probability difference widens, depending on the fit probability of L product. If the fitness probability difference widens, the intermediary is more likely to adopt ascending display order whena L is small; while it is more likely to adopt descending display order whena L is large. The different effect is due to the non-monotonic effect ofa L . 4.3 Conclusion Online shopping intermediaries play a major role in booming today’s online retail business by providing platforms for sellers and consumers to interact with each other. It is believed that intermediaries create values by helping consumers to find their desirable products with reduced efforts. For example, to facilitate search, intermediaries often first display the pop- ular products that are more likely to meet consumers’ tastes in the search results. However, evidence shows that they might purposely do the opposite by diverting consumers’ attention to some less popular ones by displaying them first in the search results. This is puzzling because intuitively consumers would like to pay high prices if they don’t have to search intensively to find their preferred products and this benefits sellers and intermediaries due to the revenue sharing scheme (e.g. commission fees). In this paper, we propose a equilibrium model with an intermediary, sellers, and consumers and attempt to provide a potential inter- pretation for this puzzle. Our main findings show that the intermediary sometimes may have 89 to first display in the search results the less popular products that are less likely to fit con- sumers’ needs because it needs to consider the strategic interactions between sellers. Specif- ically, when search costs are low, the intermediary chooses to first display the less popular products because this product display order can soften the price competition between sellers. However, the intermediary chooses to first display the more popular ones when search costs are sufficiently high. We also show that products’ fit probabilities affect the intermediary’s incentive in choosing the product display order. There are some relevant avenues for further research. First, the current analysis focuses on a monopoly intermediary and this provides some insights for the market with the presence of a dominating intermediary. For example, Taobao.com takes 90% of the C2C market 4 . However, in the case of duopoly intermediaries, they need to consider consumers’ participa- tion decisions when designing the product display order, which deserves further explorations. Second, it might be interesting to study the strategic consideration of shopping intermediary in the design of product display order contingent on sellers’ prices (e.g. prices from low to high or prices from high to low) and consumer search and the sellers’ competition in these search environment. Last, consumer search is often multi-dimensional. Specifically, in addi- tion to the choice of how many products to evaluate, consumers can also decide how many products to evaluate within a seller’s product line (Liu and Dukes, 2013) or determine how deeply to look into a specific product (e.g. the number of inspected attributes) (Dukes and Liu, 2015). Consumers’ information acquisition is often contingent on the specific search environment. Future research might want to explore how the product display orders are affected when consumers can search along multiple dimensions. 4 Economist, 2014. Alibaba: The world’s greatest bazaar. http://www.economist.com/news/briefing/21573980- alibaba-trailblazing-chinese-internet-giant-will-soon-go-public-worlds-greatest-bazaar 90 Figure 4.1: a snapshot of search results of laptops on Alibaba’s Taobao Mall Appendix Proof of Lemma 1 Seller j ( j= H=L) can charge high prices and obtain profit only from his non-switchers. This profit is given by p j (p j )=(1a j )a j ˜ p j (p j ) where ˜ p j (p j )= p j (1 p j ). The highest price that seller j is willing to charge is given by ¯ p j = ¯ p= 1 2 which is obtained by maximizing ˜ p j (p j ) and seller j does not want to choose any prices higher than ¯ p j . Let p j be the lowest price that seller j chooses. At this price, seller j may get both his non-switchers as well as the switchers and its profit is at mosta j ˜ p j (p j ). Solvinga j ˜ p(p j )= (1a j )a j ˜ p j ( ¯ p j ), one can obtain the lowest price p j = 1 2 (1 p a j ) and verify that p H > p L becausea H >a L . With zero search costs, consumers have perfect information about product fit and prices, implying that seller L can become more profitable by increasing its lowest price until p L = p H . This is true because by charging any price lower than p H , seller L cannot increase consumer demand. Thus, in equilibrium, p H = p L = p = 1 2 (1 p a L ). For any price 91 Figure 4.2: Illumination of the total profit of the two sellers - search cost relationship p2(p; ¯ p), in equilibrium, both sellers should be indifferent and obtain the same profit. One can verify that in equilibrium seller H chooses p H 2(p; ¯ p) with unconditional cdf F H (p) and ¯ p with probabilityb and seller L chooses p L 2(p; ¯ p) with cdf F L (p), where F L (p)= 1 a L ˜ p(p) ˜ p(p) ˜ p(p) ; b = 1 a L a H ; F H (p)= 1 a H ˜ p(p) ˜ p(p) ˜ p(p) : Given these distributions, one can verify that the expected profits for H product and L product are respectively given by a H (1a L )=4 and a L (1a L )=4, implying thatH product is more profitable than L product. 92 Proof of Lemma 2. Similar to the results in Lemma 1, the sellers highest prices are equal, ¯ p H = ¯ p L = 1 2 , and one can verify f des ( ¯ p L ) > ¯ p H . This implies that there are three possible situations that we need to discuss: 1. f des (p L ) < p H , 2. f des (p L )2[p H ; ¯ p H ], and 3. f des (p L ) > ¯ p H , where p H = 1 2 (1 p a L ) and p L = 1 2 (1 p a H ) are respectively seller H and seller L’s lowest prices that are obtained by solving p j (1 p j )= 1 4 (1a j ). Because search cost is the focal variable in our discussion, we rewrite these conditions of the three situations in terms of search costs based on the definition of f des () in section 2.2. Specifically, let t 1 and t 2 be respectively determined by f des (p L )= p L +t 1 =a L = p H and f des (p L )= p L +t 2 =a L = ¯ p H . This yields, t 1 = a L ( p a H p a L ) 2 and t 2 = a L p a H 2 Because search cost is continuous, one can rewrite the conditions of the three situations as follows: 1. t <t 1 , 2. t 1 tt 2 , and, 3. tt 2 . Next, we discuss the equilibrium price of the three situations. Situation 1. With small search cost (t <t 1 ), seller L does not want to choose any price lower than f 1 des (p H ) or higher than f 1 des (¯ p H )because doing so cannot increase demand. In equilibrium, sellerH chooses p H 2[p H ; ¯ p H ) with cdf F H and ¯ p H with probability b. Seller L chooses p L 2[ f 1 des (p H ); f 1 des ( ¯ p H )] with cdf F L . Seller H’s profits are given by a H ˜ p(p H ), (1a L )a H ˜ p( ¯ p H ), and [(1 F L (p H ))a H + F L (p H )(1a L )a H ] ˜ p(p H ) respectively at prices p H , ¯ p H , and p H 2(p H ; ¯ p H ). This yields F L (p)= ˜ p( f des (p)) ˜ p(p H ) a L ˜ p( f des (p)) ; for p2[ f 1 des (p H ); f 1 des ( ¯ p H )] 93 Seller L’s profits are given by a L ˜ p( f 1 des (p H )), [(1b)(1a H )a L +ba L ] ˜ p( f 1 des ( ¯ p H )), andf(1b)F H ( f des (p L ))(1a H )a L +[(1b)(1 F H ( f des (p L ))+b]a L gp(p L ) respec- tively at prices f 1 des (p H ), f 1 des ( ¯ p H ), and p L 2[ f 1 des (p H ); f 1 des ( ¯ p H )]. This yields b = 1 ˜ p( f 1 des ( ¯ p H )) ˜ p( f 1 des (p H )) a H ˜ p( f 1 des ( ¯ p H )) F H (p)= ˜ p( f 1 des (p)) ˜ p( f 1 des (p H )) (1b)a H ˜ p( f 1 des (p)) , for p H 2[p H ; ¯ p H ] One can verify that the expected profits for product H and L are respectively given by a H (1a L ) 4 and a L (1a H )+ba H a L 4 and the total profit is given by a H +a L +(b2)a H a L 4 . Situation 2. With median search cost (t 1 tt 2 ), the minimum price for seller H is f des (p L ) because at this price he can guarantee that consumers buy his product once they find a good fit from his product. In equilibrium, seller H chooses p H 2[ f des (p L ); ¯ p H ] with cdf F H and ¯ p H with probabilityb. Seller L chooses p L 2[p L ; f 1 des ( ¯ p H )] with cdf F L and ¯ p L with prob- ability g. SellerH’s profits are given by a H ˜ p( f des (p L )), [ga H +(1g)(1a L )a H ] ˜ p( ¯ p H ), andf[g+(1g)(1 F L (f 1 des (p H )))]a H +(1g)F L (f 1 des (p H ))g ˜ p(p H ) respectively at prices f(p L ), ¯ p H , and p H 2[( f des (p L ); ¯ p H ]. This yields g = 1 ˜ p( ¯ p H ) ˜ p( f des (p L )) a L ˜ p( ¯ p H ) F L (p)= ˜ p( f des (p)) ˜ p( f des (p L )) (1g)a L ˜ p( f des (p)) ; for p2[p L ; f 1 des ( ¯ p H )] Seller L’s profits are given by a L ˜ p(p L ), (1 a H )a L ˜ p( ¯ p L ), f[b +(1 b)(1 F H ( f des (p L )))]a L +[(1b)F H ( f des (p L ))](1a H )a L g ˜ p(p L ), and [ba L +(1b)(1 a H )a L ] ˜ p( f 1 des ( ¯ p H )) respectively at prices p L , ¯ p L , p L 2[p L ; f 1 des ( ¯ p H )], and f 1 des ( ¯ p H ). This yields 94 b = 1 ˜ p( f 1 des ( ¯ p H )) ˜ p(p L ) a H ˜ p( f 1 des ( ¯ p H )) F H (p)= ˜ p( f 1 des (p)) ˜ p(p L ) (1b)a H ˜ p( f 1 des (p)) ; for p2[( f des (p L ); ¯ p H ] One can verify that the expected profits for product H and L are respectively given by a H (1a L )+ga H a L 4 and a L (1a H ) 4 and the total profit is given by a H +a L +(g2)a H a L 4 . Situation 3. With large search cost (t t 2 ), any price in the range (p H ; ¯ p H ) is suffi- ciently low to prevent consumers from evaluating product L if product H provides a good fit, implying that seller H chooses price at ¯ p H . Knowing this, seller L chooses price ¯ p L : One can verify that the expected profits for product H and L are respectively given by a H 4 and a L (1a H ) 4 and the total profit is given by a H +a L a H a L 4 . It is straightforward that seller H’s expected profit is non-decreasing in search costs. Seller L’s expected profit decreases in search costs fort <t 1 (becauseb decreases int) and is independent of search costs fort >t 1 . In addition, it can be verified that the total profit of the two sellers decreases in search costs fort <t 1 , increases in search costs fort 1 tt 2 (becauseg increases int), and is independent of search costs fort >t 2 . Proof of Lemma 3 Similarly to the results in Lemma 2, sellers’ price ranges are given by [p H = 1 2 (1 p a L ); ¯ p H = 1 2 ] and[p L = 1 2 (1 p a H ); ¯ p L = 1 2 ], and one can verify f as (p L )< p H . Depend- ing on the values of f as ( ¯ p L ) and p H , there are two possible situations: 1. f as ( ¯ p L )> p H and 2. f as (¯ p L ) p H . Because search cost is the focal variable in our discussion, we rewrite the conditions of the two situations in terms of search costs based on the definition of f as () in section 2.3. Specifically, lett 3 be determined by f as ( ¯ p L )= ¯ p L t 3 =a H = p H .This yields, t 3 = a H p a L 2 95 Because search cost is continuous, one can rewrite the condition of the two situations as follows: 1. t <t 3 and 2tt 3 . Next, we discuss the equilibrium price of the two situations. Situation 1, With small search cost (t <t 3 ), seller H can obtain switchers’ demand with any prices lower than f as ( ¯ p L ). In contrast, seller L can obtain switchers’ demand at price f 1 as (p H ). This implies that in equilibrium seller H chooses p H 2 [p H ; f as ( ¯ p L )] with cdf F H and chooses ¯ p H with probability b and seller L chooses p L 2 [ f 1 as (p H ); ¯ p L ] with cdf F L and chooses ¯ p L with probability g. One can verify that the expected profit for product H is a H (1a L ) ˜ p( ¯ p H ) and that for product L is [a L (1a H )+ba H a L ] ˜ p( ¯ p H ). Any price of a product should generate the same expected profit in equilibrium. This yields all the probabilities in equilibrium as follows b = 1 ˜ p( ¯ p L ) ˜ p( f 1 as (p H )) a H ˜ p( ¯ p L ) F H (p)= ˜ p( f 1 as (p)) ˜ p( f 1 as (p H )) a H ˜ p( f 1 as (p)) ; for p2[p H ; f as ( ¯ p L )) g = 1 ˜ p( f as ( ¯ p L )) ˜ p(p H ) a L ˜ p( f as ( ¯ p L )) F L (p)= ˜ p( f as (p)) ˜ p(p H ) a L ˜ p( f as (p)) ; for p2[ f 1 as (p H ); ¯ p L ] One can verify that the expected profits for product H and L are respectively given by a H (1a L ) 4 and a L (1a H )+ba H a L 4 and the total profit is given by a H +a L +(b2)a H a L 4 . Situation 2. With large search cost (t >t 3 ), any price in the range(p L ; ¯ p L ) is sufficiently low to prevent consumers from evaluating product H if product L provides a good fit, imply- ing that seller L chooses price ¯ p L . Knowing this, seller H chooses ¯ p H : One can verify that the expected profits for product H and L are respectively given by a H (1a L ) 4 and a L 4 and the total profit is given by a H +a L a H a L 4 . It is straightforward that the expected profit of product H is independent of search costs but that of product Lincreases in search costs. .In addition, it can be verified that the total 96 profit of the two sellers increase in search cost fort <t 3 and is independent of search costs fort >t 3 . Proof of proposition 1 From Lemma 1, when search costs are zero, the two display orders do not create any difference to sellers’ competition, implying that the total profits of the two sellers are equal. From the results of Lemma 2 and Lemma 3, one can verify that t 1 <t 2 <t 3 and the total profits of the two sellers are equal when In addition, 8 > > > > > < > > > > > : descending p H (des)+p L (des)>p H (as)+p L (as) indi f f erent i f p H (des)+p L (des)=p H (as)+p L (as) ascending p H (des)+p L (des)<p H (as)+p L (as) Next, we prove that there exists a unique cutoff search costt such that the intermediary prefers one display order for search costs lower thant and prefers the other display order for search costs higher thant . That is, we need to show that the total profit of the two sellers in one display order is higher than that in the other display order for low search cost but lower for high search cost. t 2 <t 3 . The concavity of the profit function yields ˜ p( ¯ p) ˜ p(p L ) ¯ p p L > ˜ p( ¯ p) ˜ p(p H ) ¯ p p H or equivalently ˜ p( ¯ p) ˜ p(p L ) ˜ p( ¯ p) ˜ p(p H ) > ¯ pp L ¯ pp H . The expressions of p H and p L imply a H a L = ˜ p( ¯ p) ˜ p(p L ) ˜ p( ¯ p) ˜ p(p H ) . This yields a H a L > ¯ p p L ¯ p p H or equivalently a H ( ¯ p p H )>a L ( ¯ p p L ) 97 which is the same as proving t 3 >t 2 . This result is enough to ensure that there exists a cutoff search costt such that the intermediary prefers different display orders when search cost is lower or higher than t and it is indifferent in these two display orders at t . In addition,t should fall in the range(t 1 ;t 2 ) because otherwise there exists a contradiction as the intermediary always prefers one display order over the other att . Last, we need to show thatt is unique. Specifically, we need to show the slope of total profit of the two sellers in descending display order is always higher than that in ascend- ing display order when t2(t 1 ;t 2 ). One can verify that for t 2(t 1 ;t 2 ) the total profit in descending order and ascending order is respectively given bya L (1a H ) ˜ p( ¯ p L )+a H ˜ p(p L + t=a L ) anda H (1a L ) ˜ p( ¯ p H )+a L ˜ p(p H +t=a H ). Notice that p L +t=a L < p H +t=a H when t2(t 1 ;t 2 ), the result immediately follows. Thus, there exists a unique t , which is deter- mined by a L (1a H ) ˜ p( ¯ p L )+a H ˜ p(p L +t=a L ) =a H (1a L ) ˜ p( ¯ p H )+a L ˜ p(p H +t=a H ) or equivalently (a H a L ) ˜ p( ¯ p)=a H ˜ p(p L +t=a L )a L ˜ p(p H +t=a H ) (4.1) And when t>t the total profit of the two sellers is higher in the descending display order while this total profit is higher in the ascending display order when 0<t <t . The intermediary chooses the product display order to maximize its profit. Specifically, the optimal display order is the one that creates the higher total profit of the two sellers. Thus, the intermediary selects descending display order when t>t and selects ascending display order when 0<t <t . 98 Figure 2 illustrates how the total profit of the two sellers is changing with respect tot in both display orders. Proof of proposition 2 . Plugging p H and p L in equation 4.1, 1 4 (a H a L )=a H (p L +t=a L )(1 p L t=a L )a L (p H +t=a H )(1 p H t=a H ) =( a H a L a L a H )t+(a H (1a H )a L (1a L ))=4( a H a L a L a H )t +( a H p a H a L a L p a L a H )t(a H =a 2 L a L =a 2 H )t 2 which is reduced to ( a H a 2 L a L a 2 H )t 2 ( a H p a H a L a L p a L a H )t+ 1 4 (a 2 H a 2 L )= 0 Solvingt, we get t = a H a L (a H a L )(a 3=2 H a 3=2 L ) 2(a 3 H a 3 L ) The constraint t 2(t 1 ;t 2 ) implies that the only possible solution cutoff search cost is given by t = a H a L (a H a L )(a 3=2 H a 3=2 L ) 2(a 3 H a 3 L ) Let t= p a H and s= p a L ,t is further simplified to t = 1 2 s 2 t 2 (t s) t 2 ts+ s 2 The comparative statics oft with respect to t and s are given by ¶t ¶t = s 2 t 2(t 2 ts+ s 2 ) 2 (t 3 2t 2 s+ 4ts 2 2s 3 )> 0 99 ¶t ¶s = s 2 t 2(t 2 ts+ s 2 ) 2 (2t 3 4t 2 s+ 2ts 2 s 3 ) = s 2 t 2(t 2 ts+ s 2 ) 2 [2t(t s) 2 s 3 ] ¶t ¶t > 0 implies that t always increases in a H . ¶t ¶s > 0 when s is small, and ¶t ¶s < 0 when s is large, implying thatt increases ina L when it is small and decreases ina L when it is large. 100 Reference List Victor Aguirregabiria and Pedro Mira. 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In this appendix, I list more regression results in chapter 2 for further reference. The analysis is very similar to model findings discussed in chapter 2.4. 106 Table A.1: Effect of Ratings on market share sh sh sh sh lprices -0.116 -0.072 -0.075 -0.074 (0.008)*** (0.019)*** (0.023)*** (0.023)*** rate_1 -15.705 3.216 1.935 1.697 (1.445)*** (1.198)*** (1.426) (1.430) rate1sq 1.713 -0.349 -0.206 -0.177 (0.154)*** (0.128)*** (0.152) (0.153) tmall 1.318 0.701 0.715 3.755 (0.025)*** (0.022)*** (0.024)*** (1.337)*** shipfee -0.001 -0.001 (0.000)*** (0.000)*** credit_card 0.012 0.012 (0.015) (0.015) cam_num -0.002 -0.002 (0.000)*** (0.000)*** prepay 0.000 0.000 (0.000)*** (0.000)*** store_dur 0.001 0.001 (0.000)** (0.000)** rate1tmall -0.632 (0.278)** _cons 39.139 -4.456 -1.673 -1.203 (3.407)*** (2.833) (3.358) (3.364) R 2 0.16 0.51 0.50 0.50 N 17,119 17,119 14,339 14,339 * p< 0.1; ** p< 0.05; *** p< 0.01 107 Table A.2: Effect of Ratings on market share: fixed effect sh sh sh sh lprices -0.072 0.001 -0.110 -0.111 (0.019)*** (0.059) (0.068) (0.068) rate_1 3.216 1.439 0.298 0.119 (1.198)*** (1.924) (2.007) (2.011) rate1sq -0.349 -0.191 -0.076 -0.054 (0.128)*** (0.207) (0.217) (0.218) tmall 0.701 0.532 0.570 2.969 (0.022)*** (0.026)*** (0.028)*** (1.679)* rate1tmall -0.499 (0.349) _cons -4.456 -0.156 3.988 4.331 (2.833) (4.493) (4.692) (4.698) R 2 0.51 0.83 0.82 0.82 N 17,119 17,119 14,339 14,339 * p< 0.1; ** p< 0.05; *** p< 0.01 108 Table A.3: Effect of Ratings on market share: IV sh sh sh sh lprices_hat -0.035 0.009 0.033 0.033 (0.022) (0.024) (0.030) (0.030) rate_1 -14.097 3.668 2.302 2.061 (1.459)*** (1.199)*** (1.428) (1.432) rate1sq 1.525 -0.399 -0.248 -0.218 (0.155)*** (0.128)*** (0.152) (0.153) tmall 1.368 0.705 0.720 3.778 (0.025)*** (0.022)*** (0.024)*** (1.338)*** rate1tmall -0.635 (0.278)** _cons 35.075 -6.153 -3.395 -2.912 (3.458)*** (2.844)** (3.375) (3.381) R 2 0.15 0.51 0.50 0.50 N 17,119 17,119 14,339 14,339 * p< 0.1; ** p< 0.05; *** p< 0.01 109 Table A.4: Effect of Ratings on market share: FEIV sh sh sh sh lprices_hat 0.009 0.141 -0.037 -0.044 (0.024) (0.177) (0.188) (0.188) rate_1 3.668 1.406 0.252 0.075 (1.199)*** (1.924) (2.008) (2.012) rate1sq -0.399 -0.187 -0.069 -0.047 (0.128)*** (0.207) (0.217) (0.218) tmall 0.705 0.533 0.570 2.958 (0.022)*** (0.026)*** (0.028)*** (1.679)* rate1tmall -0.497 (0.349) _cons -6.153 -1.307 3.384 3.778 (2.844)** (4.704) (4.927) (4.934) R 2 0.51 0.83 0.82 0.82 N 17,119 17,119 14,339 14,339 * p< 0.1; ** p< 0.05; *** p< 0.01 110
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Three essays on agent’s strategic behavior on online trading market
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