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Essays on quality screening in two-sided markets

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Essays on quality screening in two-sided markets

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Content ESSAYS ON QUALITY SCREENING IN TWO-SIDED MARKETS by JIN WANG 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 JIN WANG Dedication I would like to dedicate this dissertation to: My parents, for giving me unconditional love and support My husband and best friend, Chang, for encouraging me to chase my dream ii Acknowledgments I am deeply indebted to many people who have helped me to make this dissertation possible. First and foremost, I would like to express my sincerest gratitude to my advisor, Pro- fessor Guofu Tan, for his continuous advice, guidance and encouragement. In the course of my dissertation research, he was always there to support me with his professional knowl- edge and great patience. Without the countless inspiring discussions with him, I would never have made this research possible. I also own a lot of appreciation to my qualifying and my dissertation committee mem- bers, Professors Harrison Cheng, Anthony Dukes, Geert Ridder, John Strauss, Simon Wilkie, for giving me invaluable comments and suggestions, from how to improve my work, to how to present my work. My thanks also extend to many professors, including but not limited to Juan Carrillo, Cheng Hsiao, Michael Magill, Roger Moon, Jeff Nugent and Yuwei Xie, for their advice on my research and job-market. I want to thank Cheng Chou, Shuyang Sheng, Qi Sun, Fei Wang, Haojun Yu and many other friends and colleagues at USC, for the happy time and enjoyable academic debates we had together. I am also very grateful to Young Miller and Morgan Ponder for helping me with the administrative issues in the past years and making my PhD life much easier. iii Last but not least, I would like to express my deep appreciation to my beloved parents and husband, whose love leads me through frustrations and always keeps me going forward. iv Table of Contents Dedication ii Acknowledgments iii List of Tables vii List of Figures viii Abstract ix Chapter 1: Introduction 1 Chapter 2: Platform Screening and End-Users’ Choices: Theory and Evidence from Online-Trading Platforms 8 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.2 Theoretical Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.2.1 Players and Payoffs . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.2.2 Sequence of the Game . . . . . . . . . . . . . . . . . . . . . . . . 21 2.2.3 Equilibrium Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 22 2.3 Structural Model and Estimation Strategy . . . . . . . . . . . . . . . . . . 27 2.3.1 Model Specification . . . . . . . . . . . . . . . . . . . . . . . . . . 28 2.3.2 Simultaneous Entry Game . . . . . . . . . . . . . . . . . . . . . . 32 2.3.3 Estimation Strategy . . . . . . . . . . . . . . . . . . . . . . . . . 37 2.4 Data and Estimation Results . . . . . . . . . . . . . . . . . . . . . . . . . 41 2.4.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 2.4.2 Data Description . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 2.4.3 Estimation Results . . . . . . . . . . . . . . . . . . . . . . . . . . 52 2.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 Chapter 3: Optimal Screening Standard 62 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 3.2 Model Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 3.2.1 Heterogeneous Sellers . . . . . . . . . . . . . . . . . . . . . . . . 64 3.2.2 Platform Screening . . . . . . . . . . . . . . . . . . . . . . . . . . 65 3.2.3 Consumer’s Purchase Decision . . . . . . . . . . . . . . . . . . . . 66 3.2.4 Seller’s Profit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 v 3.2.5 Platform’s Profit . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 3.2.6 Sequence of the Game . . . . . . . . . . . . . . . . . . . . . . . . 68 3.3 Equilibrium Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 3.3.1 No Screening . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 3.3.2 Screening . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 3.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 Bibliography 89 Appendix A: Appendix to Chapter 2 92 Appendix B: Appendix to Chapter 3 100 vi List of Tables 2.1 Variable Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 2.2 Comparisons between Tmall and Taobao . . . . . . . . . . . . . . . . . . . 47 2.3 The Proportion of Tmall Sellers, By Rating Group . . . . . . . . . . . . . . 52 2.4 Comparisons between Tmall and Taobao, By Rating Group . . . . . . . . . 53 2.6 Counterfactual: Change of Consumer Utility . . . . . . . . . . . . . . . . . 58 2.5 Estimation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 vii List of Figures 2.1 The Distribution of Prices on Tmall and Taobao . . . . . . . . . . . . . . . 49 2.2 The Distribution of Rating Score on Tmall and Taobao . . . . . . . . . . . 50 2.3 Sellers’ Choices of Platforms, By Rating Score . . . . . . . . . . . . . . . 51 2.4 Distribution of Prediction Errors, Sellers’ Choice Probabilities . . . . . . . 56 3.1 The Equilibrium without Screening . . . . . . . . . . . . . . . . . . . . . . 73 3.2 The Equilibrium with Screening . . . . . . . . . . . . . . . . . . . . . . . 77 viii Abstract In two-sided markets, consumers care not only about the number of sellers with which they can interact, but also about the quality of products or services these sellers provide. Previous work on two-sided markets has mainly focused on the quantity externality; Little attention has been paid to the quality externality. In this dissertation, I allow both quality and quantity play a role in the end-users’ interactions, and analyze how platforms can use quality screening to alleviate the problem of asymmetric information of quality and moti- vate end-users’ participations; and discuss how a platform can implement quality screening and choose optimal quality standard. The first essay examines the impact of quality screening on end-users’ choices in a con- text of competitive platforms. The analysis proceeds from both theoretical and empirical perspectives. In the theory, I build a model in which two platforms compete but only one of them screens sellers’ products. I show that the quality screening influences consumers’ expectations of product quality and their choice of sellers and platforms. The resulting screening effect, together with the network and competition effects, further drives sellers to enter different platforms. Comparative static analysis indicates that sellers’ incentives to join the platform that screens products follow an inverted-U curve with respect to the ix observable quality of products. In the empirical study, I transfer the theory to a simultane- ous entry game with incomplete information, and carry out the estimation using the Nested Pseudo Likelihood (NPL) estimator with the data from Tmall and Taobao, two online trad- ing platforms operated by Alibaba. The estimation results are consistent with the theory. The counterfactual analysis suggests that quality screening improves the consumers’ utility and enlarges Alibaba’s market share. In the second essay, I investigate the optimal thresholds of screening for end-users and the platform. I consider a monopoly platform which utilizes screening to select qualified products onto the market. I find that the platform’s profitably optimal screening standard falls below the one that maximizes the consumers’ welfare. And the platform prefers to implement quality screening by just informing consumers of the threshold instead of by fully revealing the products’ true quality. x Chapter 1 Introduction Many firms like eBay do their business by acting as an intermediary, or platform, which enables interactions between two groups of users: sellers and buyers. Through this or other platforms, end-users on the two sides trade products or services and realize their cross-group externality: the utility of users on one side depends on the performance of users on the other side. The platform operator profits by collecting usage fees from end- users onboard. In this economy, both end-users’ benefits and the platform’s profits depend heavily on how well the platform can help users to exploit their cross-group externality. This externality can involve end-users’ interdependence in two dimensions: quality and quantity. For instance, when a consumer visits an online trading platform, she cares not only about the number of sellers available to choose from but also about the quality of products these sellers provide. Previous studies of two-sided markets have mainly focused on the quantity external- ity: a user’s utility is purely determined by the number of users on the other side. Less attention has been paid to end-users’ quality concerns. When users evaluate the benefit of participating in a platform, they often take into account the quality of service and product exchanged in the interaction. If users know they may have interactions of poor quality, they will likely reduce the usage of the platform. The situation worsens if there is asymmetric information in quality between users on two sides. Following the classical economic theory 1 since Akerlof (1970), asymmetric information can result in end-users’ adverse selections and impede interactions which could have benefited users on both sides. Given the empha- sis users place on quality, platform providers have a strong incentive to manage end-users’ quality. In this dissertation, I allow both quality and quantity play a role in the end-users’ inter- actions, and analyze how platforms can use quality screening to alleviate the asymmetric information problem and motivate end-users’ participation. Quality screening has a pop- ular application in two-sided platforms: Prestigious shopping malls carefully select the brands that are going to enter the mall. Many academic journals maintain good reputations and large readership because they have a rigorous refereeing process. In spite of the broad use of quality screening in two-sided markets, there have been few studies to investigate the economic implications of screening for players’ choices and welfare. For instance, does screening benefit platform providers? How does quality screening affect end-users’ interactions? If there are two platforms with different quality screening standards, which platform will users choose? And how can a platform implement quality screening and choose optimal screening standard? My study will address these questions. In Chapter 2, I examine the choices of end-users, specifically, consumers and sellers, when they face duopoly platform competition in which one platform uses quality screening and the other does not. The analysis is composed by two parts: theoretical and empirical study. In the theory, the main challenge is that quality screening influence end-users’ participa- tion of platforms and post-entry interaction. The two aspects are interdependent and need to be modeled together. I characterize the consumer’s equilibrium belief about a seller’s 2 quality, their choices of sellers and platforms; and derive the seller’s equilibrium participa- tion of the platform. I show that the seller’s choice is determined by three effects: screening effect, competition effect and network effect. In the comparative analysis, I show that when a seller’s observable quality increases, its inventive to join the platform which uses quality screening could take an inverted-U curve: first increases and then decreases. Then I apply the theory to the empirical study. I prove that the previous theory can be equally transferred to a static entry game where sellers simultaneously choose the platform with imperfect information about other sellers’ quality. So the model can be estimated using the NPL estimator proposed by Aguirregabiria and Mira (2007). I implement the estimation with the data collected from Alibaba’s two shopping sites: Tmall and Taobao, and have two main findings: first, my work identifies the parameters about the consumer’s and seller’s participation and interaction, especially the screening, competition and network effects. The signs of parameters are consistent with the predictions of previous theory. Second, I conduct counter-factual analysis and study what if Alibaba does not use quality screening. I find that if Alibaba removed quality screening, its comparative market share would substantially decrease. In Chapter 3, I aim to quantify the optimal quality screening standard from the prospec- tive of end-users and the platform. I consider a monopoly platform which serves homoge- neous consumers and heterogeneous sellers, the latter of which hold private information of their products. The platform is able to fully observe the quality of the product through qual- ity screening and decides whether to allow the seller to enter, depending on whether or not the quality of the product exceeds the quality standard. Consumers observe the platform’s screening standard and sellers’ observable quality, and update their belief of the quality and 3 make their entry and purchase decisions.This paper shows that as the screening standard varies, there exists either a pooling or separating equilibrium about the sellers’ participa- tion of the platform. For the consumers, the payoff of joining the platform is maximized if the screening standard equals to the consumer’s reservation value. In order to motivate the participation on both sides, the platform sets the quality standard less than the reservation value. Compared to fully revealing the product’s quality to consumers, the platform finds it more profitable to just inform consumers of a quality threshold. Literature Review. This study contributes to the literature of two-sided markets and network externalities (Katz and Shapiro (1985, 1986); Laffont et al. (1998a,b); Rochet and Tirole (2002, 2006); Caillaud and Jullien (2003); Armstrong (2006); Weyl (2010)). The two-sided markets are featured by the interactions between two groups of agents with cross-group externalities. To make profits, platforms need to solve the so-called “Chicken- and-Egg” problem and “get both sides on board” (Caillaud and Jullien (2003); Rochet and Tirole (2003); Rysman (2009)). That is, when platforms design their business strategies, they should consider the responses of agents on both sides. Existing literature studies the mechanism design on two-sided markets from various perspectives, which include the pricing schemes and prices allocation on both sides (Rochet and Tirole (2003, 2006); Arm- strong (2006)), platforms’ price commitments (Hagiu (2006)), price discrimination and bundling (Damiano and Li (2007); Chao and Derdenger (2013)), exclusive contracts (Arm- strong and Wright (2007)), platform or end-users coordination (Rochet and Tirole (2002); Ambrus and Argenziano (2004)) and so on. These studies, although addressing different questions on two sided markets, usually focus on the quantity externality: the utility of a user on one side depends only on the number of users on the other side. There are papers 4 which allow end-users to have heterogeneous benefits from interactions, but this hetero- geneity in their models is assumed pre-determined and does not change with platform’s decision. The importance of quality in end-users’ interactions is rarely mentioned. My study proposes a model which captures end-users’ interdependence on both quality and quantity. In this framework, I study how a platform can use quality screening to alleviate the problem of asymmetric information between end-users and prompt end-users’ interac- tions and the platform’s profit This paper also joins the empirical study of two-sided markets. Some previous work has identified the network effect between end-users in different two-sided markets (Rysman (2004, 2007); Ackerberg and Gowrisankaran (2006); Argentesi and Filistrucchi (2007)). Lee (2013) develops a dynamic model to study consumers’ purchases of hardware and software, and software providers’ adoption on hardware, and the welfare implication if the integration and exclusive contract between hardware and software is prohibited. Zhou (2013) proposes a new method to estimate consumers’ and software providers’ decisions and points out the hardware firms’ pricing leverages on the two sides are important for the platforms’ launch success. In this study , I build a structural model to estimate consumers’ choices and sellers’ entry decisions. When they make decision, both consumers and sellers take into account the impact of quality screening on their utility and profits. My work identifies the network, competition and screening effects in the interactions between sellers and buyers. 5 This research is also closely related to the literature of the estimation of discrete choice games and its applications. This stream of literature starts from the seminal work by Bres- nahan and Reiss (1990, 1991) and Berry (1992). They analyze firms’ strategic entry deci- sions in the framework of a discrete choice game. Stavins (1995), Mazzeo (2002) and Toivanen and Waterson (2005) adopt the same framework and study firms’ entry deci- sions in different scenarios. All these papers perform their study under the assumption that firms possess complete information of rivals’ characteristics. During the estimation pro- cess, researchers have to check every firm’s equilibrium conditions, which increases the computation burden, especially when the number of firms and their alternative choices are very large. In many applications, firms do not completely know other firms’ decision vari- ables. This makes the incomplete-information structure a more favorable choice. Under the structure of incomplete information, firms’ equilibrium choices can be formalized as a set of Bayesian Nash equilibrium beliefs and the estimation gets easier (Rust (1996)). Estimators proposed by Hotz and Miller (1993), Aguirregabiria and Mira (2002, 2007), Pesendorfer and Schmidt-Dengler (2008) and Pakes et al. (2007) are easily implemented in games with a large number of players or alternative choices. The discrete game with imperfect information has many applications including the empirical study of firms’ entry and special competition (Seim (2006); Zhu and Singh (2009); Vitorino (2012)) and social interactions (Brock and Durlauf (2001)). In my paper, I show that the theoretical model can be equally transferred to a discrete choice game where sellers simultaneously enter different platforms with imperfect information of rivals’ quality. Unlike previous studies of entry games which assume abstract profit functions for entrants, I derive sellers’ profit functions from the theoretical model which captures the interactions between sellers and 6 buyers. Estimation is carried out by using NPL estimator proposed by Aguirregabiria and Mira (2007). 7 Chapter 2 Platform Screening and End-Users’ Choices: Theory and Evidence from Online-Trading Platforms 2.1 Introduction In this chapter, I study quality screening in the context of online trading platforms, serving two types of end-users: sellers and buyers. Within a platform, sellers compete in selling a particular product to consumers. The quality of products is heterogeneous and composed of two parts: the quality observable to all players and the private quality signal known only by the seller. To overcome the information asymmetry, the platform can implement quality screening by charging sellers different usage fees depending on their products’ qual- ity. More specifically, the platform collects each seller’s quality information by randomly sampling products or through consumer feedback. The quality signal the platform obtains mixes the true product quality plus a noise term. If the value of the signal lies above a threshold, the platform offers the seller a discount on the usage fee. Otherwise, the plat- form charges the seller a high usage fee and reduces the seller’s profit to zero. Under this 8 rule, the higher the product quality is, the more likely the seller will enjoy a lower platform usage fee. To investigate the effect of quality screening on buyers’ and sellers’ entry decisions, I assume two platforms in the model. One platform employs quality screening as described above and I denote it as Platform S. The other platform is a free-entry market and refers to Platform NS. Both buyers and sellers are single-homing. The model illustrates that the number of consumers on a platform depends on the total utility provided by the entire seller group on a platform. That is, the platform which gathers more sellers of better quality can seize a larger market share on the consumer side. On the seller side, a merchant’s loca- tion decision is governed by three effects: screening, network and competition. First, the screening effect means that sellers can convince consumers that their products are of good quality, by showing their willingness to pay a usage fee correlated with quality. Entering Platform S enables a seller to signal the unobserved quality of the product and increase the chances of sales. The network effect and competition effect characterize two ways that a seller’s participation decision is influenced by the number of consumers on the platform. On one hand, a merchant wants to enter the platform with a larger number of consumers. By interacting with more consumers, the merchant can sell more products. On the other hand, the number of consumers on a platform is positively correlated with the utility provided by the entire seller group. So for a seller, joining a platform which has more consumers means that it has to face fiercer competition. This may reduce this seller’s market share. The relative magnitude of two effects determines how a seller responds to the consumers’ par- ticipation. If network effect dominates, a seller is willing to join the platform that attracts 9 more consumers. Otherwise, the seller would rather avoid peer competition by choosing the platform which has fewer consumers. Under the influence of the screening effect, the proportion of sellers choosing Platform S first increases with the observable quality. Once the observable quality reaches a certain point, the network and competition effects take over and may reduce the proportion of sellers on Platform S. The intuition works as follows: For a merchant that sells a product of low or medium observable quality, entering Platform S can signal the product’s unobserved quality and increase sales. But this may also bring the risk of paying a high usage fee if the product fails Platform S’s quality screening. When the observable quality increases, the product is more likely to meet the standards of Platform S and therefore the sellers will be more willing to enter this platform. If the product is of sufficiently high observable quality, a seller will not worry about passing the quality screening. The unobserved quality of the product can not be inferred by consumers regardless of the platform the product is located on. So the screening effect vanishes and only the competition and network effects matter in the sellers’ decisions. The seller chooses its desired platform by weighing the comparative magnitude of both effects. To test the theory, I apply the two-sided market model to the empirical study. By doing this, I am able to estimate the end-users’ responses to quality screening and quantify the impact of screening on the profits of the platform provider. I select Alibaba because of both its size and business strategy. Firstly, Alibaba is a monster E-commerce firm. It has so far captured over 90% of the online market in China. In 2013, its total sales were $248 billion dollars – more than eBay and Amazon combined. Second, Alibaba operates two online- trading platforms: Taobao and Tmall. Taobao is a free-entry market where any product 10 can be posted for sale, while Tmall sets a quality standard and charges sellers usage fees depending on their quality. Therefore, Taobao and Tmall are exactly the counterparts of Platform NS and Platform S in the theory, and their business models fit the setup of my theory well. The data is collected from these two websites. It contains sellers’ information including each seller’s rating score, price, monthly sales and location (Tmall or Tabao). The variable rating score is treated as the proxy of the seller’s observable quality. In the data, as the rating score increases, the proportion of sellers that choose Tmall first increases then decreases, which is consistent with the prediction of the theory. To proceed with the estimation, I show that the two-sided market model can be equally formalized as a game in which sellers simultaneously choose their desired platform with incomplete information about other sellers’ quality. Unlike previous entry games which mostly assume that sellers have abstract profit functions, my two-sided market model pro- vides a well-defined profit function which incorporates consumers’ belief of a seller’s qual- ity conditional on the seller’s location choice, rival sellers’ location choices probabilities, and the seller’s entry cost. Sellers’ equilibrium choices in the two-sided market model are readily transformed into a set of Bayesian Nash equilibrium choice probabilities. These probabilities are a fixed point, which is determined by the mapping from a seller’s conjec- ture of competitors’ choices to its competitors’ conjectures of this seller’s choice. And they are to be estimated together with the seller’s profit function. The estimation is carried out using the Nested Pseudo Likelihood (NPL) estimator pro- posed by Aguirregabiria and Mira (2007). In the demand function, the total utility provided by the entire seller group has a parameter of positive sign. It suggests the network effect 11 dominates the competition effect and sellers benefit from pooling with rivals of good qual- ity. The impact of the expected unobservable quality on a seller’s demand varies by seller types. For sellers with low or medium rating scores, the estimator is positive and signifi- cant, while for sellers with high rating scores, the estimator is negative and close to zero. This supports my theory that in equilibrium the screening effect only takes effect on sellers of low and medium observable quality. These types of sellers can convince consumers that their products are of good quality if they submit to the quality screening of Tmall. In the entry cost function, the estimation results indicate that a seller of a higher rating score or higher unobservable quality pays a lower usage fee on Tmall, which coincides with the spirit of quality screening. Last, I conduct a counterfactual analysis to investigate whether the strategy of market separation and quality screening can improve consumers’ welfare and also help Alibaba to achieve more advantageous position when it competes with rival firms. I construct a vari- able which compares the consumer’s expected utility from all sellers located on Alibaba before and after Alibaba would remove quality screening. I find that the total utility pro- vided by the entire seller group gets increased with the presence of quality screening. This also means, by employing quality screening, Alibaba to some extent improves its market position. The rest of the chapter is organized as follows. Section 2 presents the theoretical model and derives the equilibrium choices of game players. Section 3 transfers the theoretical model to a simultaneous entry game with incomplete information and discusses the esti- mation strategy. Section 4 firstly introduces the background of Alibaba and its two online 12 trading platforms: Tmall and Taobao, discusses the data, and then presents the results of estimation and counterfactual analysis. Section 5 concludes the chapter. 2.2 Theoretical Model 2.2.1 Players and Payoffs I study two-sided online trading markets. It is easy to generalize the results of my model to other two-sided platforms which use quality screening to regulate users’ entry and interac- tion. There are three types of players in the game: sellers, buyers and the platform provider. I will discuss their characteristics in this subsection: Product Quality There are N (N >> 0) sellers in the model. They compete for selling the same product to consumers. Sellers are heterogeneous in their product’s quality. Denote the quality of products sold by seller j as q j . It is composed of two parts: q j =m j +q j (2.1) where m j is the observable quality of the product. Think about a merchant that sells a camera, say Nikon D3300, m j can be the camera’s specs, the seller’s reputation, or other observable characteristics. u j is fixed and perfectly observed by all players. I do not con- sider the case in which the seller can manipulate or hide the information of m j to cheat consumers and platforms. m j satisfies Assumption 2.1. 13 Assumption 2.1 (Observable Quality) The observable qualitym satisfies: (i)m2(¥;+¥). (ii) Among the N sellers, the number of sellers withm = x is N x . The second component,q j , is the private information about the quality of the product. q j is known only by seller j. Back to the previous example, the camera could be a fake or refurbished product, or its flash button does not function very well. This information is concealed by the seller for its own interest. Platforms and consumers have a prior on the value of q j , which is drawn from a distribution whose properties are common knowledge and satisfy Assumption 2.2. Assumption 2.2 (Independent Symmetric Private Signal) The distribution ofq satisfies: (i). q is independent withm. (ii). q f q where f q is a log-concave continuous function on the closed interval[q;q]. (iii). q has a mean of zero:E(q)= 0. m and q are assumed to be independent with each other. It means that platforms and consumers are not able to completely infer the value of the private quality signal from the observable characteristic. My model can allow a random correlation betweenm andq and this does not change the main results. The assumption of log-concave distribution is made for the comparative static analysis. The family of log-concave probability distributions has broad applications in economics (Heckman and Honore (1990); An (1996); Bagnoli and Bergstrom (2005)). It includes many commonly-used distributions such as normal distri- bution and exponential distribution. The zero-mean assumption is made for normalization. 14 Platforms and Quality Screening In the model, there are two platforms, which are denoted asfS;NSg perceptively. My model assumes that two platforms are operated by the same company, but differentiate in their usage fees and quality screening policies. Platform S and quality screening. Platform S screens sellers’ products for quality and charges sellers different usage fees varied by the screening results. It monitors the quality all products sold on the platform, and collects the quality information from three resources: consumers’ feedbacks, the quality inspection by the official department of the government, or the random sampling test by Platform S itself. To be specific, Platform S can encourage consumers to provide feedbacks about the products they bought from the platform and learn the quality. Second, when the commercial administration department of the government inspects sellers’ products, the inspection results can also inform Platform S of the quality information. Last, Platform S can request sellers to submit sample products and check their quality. Through above three channels, Platform S obtains a noisy quality signal ˆ q j for the product sold by seller j: ˆ q j = q j +e j = m j +q j +e j (2.2) in which q j is seller j’s true quality specified in 2.1 and e j represents a random shock to the quality of the product. For instance, back to the previous example of cameras,e j can be 15 understood as the uncontrollable factors taking place during a camera’s production, storage or delivery, which influences the judgment or evaluation of the quality of the product. In the model,e j is assumed to be a realization of a random variablee, the distribution of which is common knowledge to all players. Assumption 2.3 (Independent Quality Shock) The distribution ofe satisfies (i)e is independent ofm andq; (ii)e f e and f e is a continuous function on[e; ¯ e]. Based on the quality signal ˆ q j , Platform S charges sellers usage fees. The usage fee is assumed to be proportional to the seller’s total transaction value, and the proportion ˆ t S is determined by ˆ t S = 8 > > > < > > > : t S if ˆ q j k S 1 if ˆ q j < k S where t S 2(0;1) and k S represents a quality standard set by Platform S and known by all other players. This formula illustrates that the proportional fee imposed on seller j depends on the quality signal ˆ q j . If ˆ q j exceeds the quality standard k S , Platform S only takes away t S percent of the revenue of seller j. If ˆ q j lies below k S , it means seller j’s product fails to meet the quality requirement, and as a result, the seller loses all the transaction revenue to the platform. To sum up, Platform S screens sellers’ products and charges its sellers transaction fees which depend on whether the sellers can pass the screening. 16 Platform NS: Platform NS charges sellers a uniform proportional fee t NS 2[0;1). This is equivalent to the case that Platform NS implements quality screening, but sets the stan- dard k NS =¥ such that every seller can pass the screening. Consumer’s Decisions The measure of potential consumers is normalized to be one. Consumers are homogeneous and single-homing. They make independent entry and purchase decisions which can be summarized as the following two steps. Firstly, the consumer decides which marketplace it visits among three options: Platform S, Platform NS, and the outside option which is denoted as 0. After choosing the market, the consumer makes the second-step decision: it evaluates the utility obtained from the sellers on that marketplace and purchases one unit of the product through the seller which offers the consumer the largest utility. In this subsection, I model the consumer’s two-step decision in a backward sequence: first discuss the purchase decision and then analyze the entry. Consumer’s Purchase Decision LetJ(m) denote the set of sellers on the platform m where m2fS; NSg, consumer i obtains a random utilitye u i; j;m through purchasing the product from the seller j2J(m), wheree u i; j;m takes a linear form: e u i; j;m =E(q j jm j ; m) price j +e i; j;m (2.3) 17 whereE(q j jm j ; m) represents the consumer’s belief about the seller’s product quality con- ditional on the observable qualitym j and the platform the seller is located on . And price j is the price of the product. e i; j;m : all j2J(m) are i.i.d. seller-specific random utility shocks following Type-I extreme value distribution f e (0;1;0), which are independent ofm andq . Define u j;m =E(q j jm j ; m) price j as the consumer’s expected utility of shopping from the seller j2J(m). The probability that the consumer i buys from seller j can be expressed as: d jj j2J(m) = Pr(e u j;m e u j 0 ;m ; all j 0 2J(m)) = exp u j;m å all j 0 2J(m) exp u j 0 ;m (2.4) . It shows that within a platform, a merchant which provides higher utility can attract more consumers. Besides, this probability is negatively correlated with the utility provided by all the sellers on the platform, which suggests that the competition among sellers becomes intensified as the total utility consumers obtain from the entire seller group increases. Consumer’s Entry Decision Consumer i’s utility of patronizing platform m : m2fS; NSg equals to: e n i;m =lEU m +h i;m 18 where EU m stands for the expected maximum utility offered by sellers located on platform m. Recall that e i; j;m follows Type-I extreme value distribution, according to Rust (1987), the expected maximum utility has a closed form: EU m = E maxe u i; j;m all j 0 2J (m) = ln å j 0 2J(m) exp u j 0 ;m ! (2.5) As for the expected maximum utility from the outside option, without loss of generality, I normalize it to be 0, i.e., EU 0 = 0. Therefore the consumer i’s utility of choosing the outside option equals to ˜ n i;0 = 0+h i;0 . h i;S ;h i;NS ;h i;0 represent the consumer i’s idiosyncratic preference for the three markets. They are randomly drawn from a Type-I extreme value distributionh f h (0; 1 l ;0), where 1 l > 0 denotes the scale of the distribution. h is assumed to be independent of EU m . The probability that consumer i goes to platform m : m2fS;NSg is d m = exp[lEU m ] 1+å m 0 2fS;NSg exp[lEU m 0] (2.6) Notice that d m is the market share of platform m in the whole market composed by Platform S, Platform NS and the outside option. And d jj j2J(m) is the probability that the consumer purchases from seller j provided that the consumer has decided to patronize platform m. 19 Using these two probabilities, I can derive the unconditional market share of seller j in the whole market: d j;m = d jj j2J(m) d m = exp[u j;m ] å all j 0 2J(m) exp[u j 0 ;m ] exp[lEU m ] 1+å m 0 2fS;NSg exp[lEU m 0] = exp[u j;m ] exp[(l 1)EU m ] 1+å m 0 2fS;NSg exp[lEU m 0] (2.7) . The consumer’s expected maximum utility on platform m, EU m , influences seller j’s market share on platform m, d j;m , in two opposing ways: First, since d m is positively cor- related with EU m , when EU m increases, there are more consumers to patronize platform m. By interacting with these consumers, sellers can increase the sales. I call this effect the network effect. On the other wide, as shown by (2.5), EU m incorporates the utility provided by all sellers on platform m. A bigger EU m means the seller faces fiercer com- petition from rivals, which in turn decreases the seller’s market share. I call this effect the competition effect. In (2.7), the relative magnitude of the network and competition effect are measured by(l1). Ifl > 1, the network effect dominates the competition effect and the seller prefers to participate in a platform which hosts more consumers. Otherwise, the seller would rather avoid peer competition by attending a platform with a smaller number of consumers. 20 Seller’s Profit and Entry Decision The profit of seller j on platform m can be expressed as p j;m (m j ;q j ; k m ;t m )=( ¯ p d j;m )(1t m ) Pr(e j k m m j q j ) (2.8) where( ¯ p d j;m ) represents the seller’s revenue on platform m and (1 t m ) is the percent of revenue the seller keeps after paying the proportional fee to the platform. The last term Pr(e j k m m j q j ) measures the effect of quality screening on the seller’s profit. The seller makes zero profit if its product does not pass the quality screening. The seller is assumed to be single-homing and joins the platform in which it can earn a larger profit. The total number of sellers on the platform m equals to N m = å j=1:::N 1[p jm (m j ;q j ; k m ;t m )p jm 0(m j ;q j ; k m 0;t m 0)] 2.2.2 Sequence of the Game The game proceeds in the following sequence: Period 0: The nature determines the quality of the product sold by seller j, q j = u j +q j , where m j is observable to all players. q j is the private information known only by the seller j. 21 Period 1: Platform m where m2fS;NSg announces the proportional fee t m , and the quality standard k m . Period 2: Sellers simultaneously choose which platform to participate in. Period 3: Consumers enter their desired platforms and make purchasing decisions. 2.2.3 Equilibrium Analysis This section analyzes the equilibrium strategies of sellers and consumers. Following the sequence of the game, the seller makes decision at Period 2. Its strategy is to choose Platform S or Platform NS, in anticipation of the consumer’s belief of its product quality and the product’s market share on each platform. The seller’s decision depends on several factors: the observable quality, m, the private quality signal,q, two platforms’ price menu ft S ;t NS g and the screening standardsfk S ;k NS g, and the expected number of consumers on two platformsfd S ;d NS g. At Period 3, consumers take actions. They patronize their favorite platforms and sellers, based on the distribution of sellers on the two platforms and the expected quality of products. In equilibrium, consumers’ belief of the private quality signalq should be consistent with the seller’s choice. Proposition 2.1 (Equilibrium) Given two platforms’ policy variablesft m ; k m jm2fS; NSgg, there always exists an equilibrium such that Consumers. Consumers participate in Platform S and Platform NS in probabilities d S ;d NS respectively. And the consumers’ belief ofq can be expressed as (i) Whenm < k S qe, 22 E(qjm; m= S)=E(qjqq * (m)) and E(qjm; m= NS)=E(qjqq * (m)) (ii) Whenm k S qe, E(qjm; m= S)=E(qjm; m= NS)= 0 Sellers. Sellers take the strategy as follows: (i) When m < k S qe, sellers enter Platform S if q q * (m) and participate in Platform NS ifq <q * (m), whereq * (m) is determined by: 0= ln 1t S 1t NS + (l 1) l ln d S d NS +E(qjqq * (m))E(qjqq * (m))+ ln(1 F e (k S mq * (m))) (ii)Whenm k S qe, sellers always enter Platform S if ln 1t S 1t NS + (l 1) l ln d S d NS > 0 , and they choose Platform NS otherwise. Proof: see in the Appendix A. 23 I sketch the equilibrium here, leaving the complete proof in the appendix. Following previous analysis, the seller makes the entry decision by comparing the profits on the two platforms, which can be expressed as : lnp S lnp NS = ln 1t S 1t NS (4proportional fee) + (l 1) l ln d S d NS (4network v.s. competition effects) + E(qjm; m= S)E(qjm; m= NS) (4screening effect) + ln(1 F e (k S mq)) (4screening cost) (2.9) . This formula shows that the seller evaluates the payoffs on two platforms from four aspects: the proportional fees, the network versus competition effects, the screening effects and screening costs. First, the seller compares the proportional fees charged by the two platforms, because these fees determine the seller’s net revenue. Second, sellers are also concerned about the network and competition effects. As discussed in Section 2.1.5, these two effects characterize the impact of the number of consumers on a seller’s profit. This impact is realized through the coordination and competition among sellers on the same platform. When a platform has more sellers of good quality, it influences the profit of indi- vidual seller in two directions: On one hand, this attracts more consumers to the platform and prompts each seller’s sales. On the other hand, it intensifies the competition between sellers and deteriorates individual seller’s profit. If (l 1) is positive, the network effect becomes dominant and the seller wants to join the platform which have more consumers. Otherwise, the seller favors the platform with fewer consumers. The screening effect arises from the fact that consumers update their belief of sellers’ unobservable quality according 24 to the platforms’ screening policies and the sellers’ participation decisions. Such an expec- tation should be higher for sellers on Platform S which adopts a higher quality standard. Although a seller can enter Platform S to signal its quality, it has to bear the risk that it may fail in the quality screening and earn zero profit. This screening cost can impede the seller’s incentive to join Platform S. In the four factors, the proportional fees and the network and competition effects are homogeneous among all types of sellers, while the magnitude of the screening effect and the screening cost vary with the quality of the product. To be specific, the screening effect depends on the observable qualitym and the platform the seller is located on. The screening cost depends on both the observablem and the private quality signalq. Sellers that hold the private quality information weigh the benefits and costs of screening and are self selected onto the different platforms. Anticipating the correlation between quality and seller’s entry decision, the consumer rationalizes the belief ofq. That’s how the quality screening mech- anism works. When the observable qualitym is less thanm < k S qe, there is positive probability that the product fails in quality screening. In this case, by submitting to the quality screen- ing of Platform S, the seller can convince consumers the product is of good quality. Since the screening cost decreases withq, the seller chooses Platform S if its private signalq is large enough. And the threshold ofq, in equilibrium, is correctly inferred by the consumer. However, the effect of screening vanishes when the observable qualitym is sufficiently high such that m k S qe. In this case, the seller always passes the quality screen- ing, which suggests q is no longer a factor that plays a role in the seller’s entry decision. Consumers are not able to update their belief of q according to the seller’s participation 25 decision. Correspondingly, on both platforms, consumers adjust the belief ofq to the pop- ulation mean: E(qjm; m= S)=E(qjm; m= NS)= 0 . Therefore the seller’s entry decision only relies on the proportional fees and the network effects on the two platforms. Proposition 2.2 (Comparative Statics) Supposeq f q where f q is log-concave, ande Exp(l) where l>1. (i) Whenm < k S q ,q * (m) is a decreasing function ofm. (ii) Whenm k S q, q * (m)= 8 > > > < > > > : q if ln 1t S 1t NS + (l1) l ln d S d NS 0 ¯ q if ln 1t S 1t NS + (l1) l ln d S d NS < 0 Proof: see in the Appendix A. This proposition illustrates there may exist a non-monotonic relationship between the observable quality and the seller’s entry decision. When the observable quality is less than k S q, a seller wants to join Platform S to take the advantage of the screening effect. At the same time, it needs to pay the cost associated with the risk of failing the screening test. Under the distribution assumptions in Proposition 2.2, whenm increases, the benefit of tak- ing quality screening outpaces the cost such that the net benefit of taking quality screening increases. Sellers that have higher observable quality are more likely to choose Platform S. Once the observable quality reaches k S q, both the benefit and cost of screening go to 26 zero. Therefore, the seller’s own characteristics, either the observable quality or the private signal, do not have any impact on the seller’s entry. The network and competition effects take over and play a key role in determining a seller’s choice of platform. The usage fees on the two platforms also matter in the seller’s decision. Sellers now become identical and make symmetric entry decisions. They may choose to enter Platform NS, if this platform provides a larger network effect or a smaller competition effect. Therefore, under the influ- ences of the screening, network and competition effects, a seller’s incentive to participate in Platform S may follow an inverted-U curve with respect tom. So far I have characterized the interactions between sellers and consumers on the two platforms and analyzed their equilibrium choices. But there is still a question which remains to be answered: Does the quality screening benefit consumers and the platform operator? Answering this question requires us to make a series of assumptions on the vari- ables in the model, which include: the number of potential sellers, each seller’s observable quality and the private signal, and the prior of the private signal and the screening noise. Instead of making these assumptions and getting an abstract answer, I choose to investigate the effect of screening on consumers’ welfare and platforms’ profits using the data from the real business. In the next section, I will discuss how to apply the model to the data and do the estimation. 2.3 Structural Model and Estimation Strategy In this section, I utilize previous theory to build a structural model and discuss the esti- mation strategy. I first show that the two-sided market model specified in Section 2 is 27 equivalent to a discrete choice game in which sellers simultaneously decide whether to enter platform m, holding incomplete information of other sellers’ quality. Then I present the estimation procedure of this incomplete information game. 2.3.1 Model Specification In order to apply the model in Section 2 to the data, I rewrite players’ payoff functions with the deterministic characteristics and associated parameters. Suppose there are T indepen- dent products. For each product, there are a particular number of sellers and consumers that play the game as described in Section 2. Consumers. I start from the consumer’s preference and utility function. A representa- tive consumer believes that the quality of product t sold by seller j takes following form: q t j = X t j a+q t j b; (2.10) where X t j is a vector of observable attributes of the seller, e.g. reputation, the dummy vari- able for free-shipping, return policies, et. al.; X t j is pre-determined and does not change with the seller’s choice of platform. q t j represents the private quality signal possessed by the seller j, for instance, the long-term reliability or the authenticity of the product. q t j is assumed to be a realization of a single random variable q whose distribution satisfies Assumption 2.2. The parametera andb measure the weights of X t j andq t j in the composi- tion of the product’s overall quality. 28 Given the quality specification, the consumer i’s utility of purchasing product t from seller j located on platform m can be expressed as ˜ u t i; j;m = u t i; j;m +e t i; j;m in which the expected utility equals to u t j;m = X t j a+E q t j jX t j ; m b+ price t j g , whereg reflects the influence of product price on the expected quality. Following the analysis in Section 2, the choice probability of seller j in the whole market of product t in (2.7) can be explicitly written as d t j;m = exp[u j;m ] exp[(l 1)EU m ] å all m 0 2fS;NSg exp[lEU m 0] (2.11) with EU m = ln å j 0 2J t (m) exp u t j 0 ;m ! = ln å j 0 2J t (m) exp h X t j 0a+E h q t j jX t j 0; m i b+ price t j 0g i ! Sellers. The seller’s profit of participating platform m in equation (2.8) can be equally summarized as p t j;m =[d t j;m price j ]G(X t j ;q t j ; m)] 29 The first term in bracket represents the seller’s sales revenue which is a product of the seller’s market share, d t j;m , defined in (2.11) and the seller’s price, price j . G(X t j ;q t j ; m)2 (0;1) stands for the fraction of revenue the seller earns net of the screening cost and the platform usage fee . According to Section 2, it is a function of the seller’s quality(X t j ;q t j ) and the index of the platform. For sellers located on Platform S,G(X t j ;q t j ; m) is positively correlated with the seller’s quality(X t j ;q t j ), while for sellers on Platform NS,G(X t j ;q t j ; m) is independent of the seller’s quality type as this platform has no quality regulation on its entrants. The profit function can be transferred to a linear function by taking logarithm on both sides: lnp t j;m = lnd t j;m + ln price j + lnG(X t j ;q t j ; m) . When the screening noisee in (2.2) follows exponential distribution, lnG(X t j ;q t j ; m) also has a linear form: lnG(X t j ;q t j ; m)=r m 0 +r m 1 X t j +r m 2 q t j . Therefore, the difference of the seller’s log-profits on the two platforms is: 4p t j lnp t j;S lnp t j;NS = lnd t j;S lnd t j;NS +r 0 +r 1 X t j +r 2 q t j (2.12) wherer k =r S k r NS k , k2f0;1;2g. And according to the rule of quality screening, it can be expected that r 1 ;r 2 > 0. That is, the seller with higher quality (X t j ;q t j ) can expect to earn more if joining Platform S. 30 With the specification of d t j;m in (2.11),4p t j can be further decomposed as following: 4p t j = ln å j 0 2J t (S) exp u t j 0 ;S ! ln å j 0 2J t (NS) exp u t j 0 ;NS ! (l 1) + E q t j X t j ; m= S E q t j X t j ; m= NS b + r 0 +r 1 X t j +r 2 q t j (2.13) . It indicates a seller’s choice of platform is determined by three terms. The first term is associated with the number sellers located on each platform and the total utility consumers obtain from these sellers. The way this term affects the seller’s profitability depends on the magnitudes of network effect and competitive effect, which are correspondingly measured byl and 1. Whenl > 1, the network effect dominates and the seller favors the platform in which sellers deliver higher total utility. Whenl < 1, the competition effects dominates and the seller wants to soften the competition by joining the platform which gathers sellers with lower quality. The second term which influences the seller’s decision isE h q t j X t j ; m i , the consumer’s conjectures of the seller’s unobservable quality, conditional on the seller’s observable attributes and participation of platform. In equilibrium, these conjectures should coincide with the seller’s optimal choice. The last term that plays a role is the costs of par- ticipating in two platforms, which depend on the observable quality, X, the private quality information,q, and two platforms’ fees which are summarized in a constant termr 0 . 31 2.3.2 Simultaneous Entry Game Sellers’ Expected Payoffs Combining (2.11) and (2.12) which respectively characterize the consumer’s and seller’s strategies, I show that the seller’s entry decision can be summarized as (2.13). It is easy to find that the game presented in Section 2 is equivalent to an entry game in which sellers simultaneously decide which platform they want to participate in. In this game, each seller makes decision according to (2.13), a formula which is ultimately determined by the seller’s own characteristics and other sellers’ observable characteristics and their entry decisions. The fact thatq in (2.13) is private information implies there is imperfect information among sellers. When a seller takes action, he can not perfectly know competitor’s choices. So the seller can only form the expectation of profits on two platforms based on a prior of competitor’s entry decisions. Therefore, seller j’s expected profits on the two platforms equals to E 4p t j X t j ;W t ; P t = E h lnd t j;S lnd t j;NS X t j ;W t ; P t i + r 0 +r 1 X t j +r 2 q (2.14) where E h lnd t j;S lnd t j;NS X t j ;W t ; P t i = E " ln å j 0 2J t (S) exp u t j 0 ;S ! ln å j 0 2J t (NS) exp u t j 0 ;NS ! jX t j ;W t ; P t # (l 1) + E q t j X t j ; m= S E q t j X t j ; m= NS b (2.15) 32 Here I define the vector P t as P t n p t j 0 : any seller j 0 of product t o where p t j 0 is the seller j’s conjecture about the probability that seller j 0 chooses Platform S. Since the private quality n q t j 0 o are independently and identically distributed, any two pairs of sellers, say seller j and seller j 0 , have the same perception of a third seller h’s private signal and its entry strategy. So the conjecture vector P t is symmetric among all sellers of product t. Denote a seller’s information set as W t n X t j 0; price t j 0: any seller j 0 of product t o which includes all sellers’ observable characteristics. Seller j chooses platform S iff E 4p t j jX t j ;W t ; P t 0 33 From the perspective of competitors and we researchers, the probability that the seller participates in Platform S is given by: p t j Pr(m= SjX t j ;W t ; P t ) = Pr(E 4p t j jX t j ;W t ; P t 0) = Pr(E lnd t j;S lnd t j;NS X t j ;W t ; P t +r 0 +r 1 X t j +r 2 q 0) = F( 1 r 2 E lnd t j;S lnd t j;NS X t j ;W t ; P t + r 0 r 2 + r 1 r 2 X t j ) (2.16) . It is easy to find that p t j varies with the seller j’s observable characteristics X t j . When the game involves a larger number of sellers and their observable signals are of multi- ple dimensions and take values on a broad interval, the vector P t can have a very large dimension, which brings difficulties to the estimation. To simplify the following analysis, I assume that X is a discrete variable which takes K possible values:fx k : k= 1;:::;Kg. Therefore, conjectures of sellers’ entry to platform S can be reduced to a K by 1 vector P t = p t k : k2f1;:::Kg . To construct the seller’s expected profit function, I still need to know the consumer’s expectation about the private quality: E h q t jx t j ; m i . Here I assume the private quality q satisfies Assumption 2.2 and follows standard truncated normal distribution on[q; ¯ q]. The truncated normal distribution is appealing here because it offers a closed-form expression 34 of the conditional expectation. According to Proposition 2.1, for a seller with observable signal x t k on Platform S, the consumer’s equilibrium belief ofq t is equal to: E q t x t k ; m= S = E q t q t q t (X t k ) = f(q t (x t k ))f( ¯ q) F( ¯ q)F(q t (x t k )) (2.17) where the second equation follows the assumption thatq is distributed as truncated normal. Recall that in equilibrium, this seller participates in Platform S with a probability p t k where p t k = Pr(q t q t (x t k ))= F( ¯ q)F(q t (x t k )) F( ¯ q)F(q) . Soq t (x t k ) can be expressed as a function of p t k : q t (x t k )=F 1 F( ¯ q) p t k [F( ¯ q)F(q)] and so doesE q t jx t k ; m= S . Similarly, the consumer’s expectation ofq on Platform NS equals to E q t x t k ;m= NS = E q t q t q t (x t k ) = f(q)f(q t (x t k )) F(q t (x t k ))F(q) (2.18) which can also be written as a function of p t k . 35 Equilibrium Since the two-sided market theory in Section 2 is equivalent to a seller simultane- ous entry game with incomplete information, the equilibrium established in Proposi- tion 2.1 of Section 2 can be rephrased as Bayesian Nash equilibrium conjectures P t = p t k : k2f1;:::Kg such that 1. Consumers. Observing the number of sellers on each platform and products’ observ- able quality, consumers form a correct expectation of q as specified in equations (2.17) and (2.18), and evaluate the payoffs from sellers and platforms shown in equation (2.4) and equation (2.6), and make choices according to (2.11) . 2. Sellers. A seller chooses between two platforms to maximize its expected profit, based on its conjecture about competitors’ entry strategies. For a seller of the observable quality type x t k , the probability that it enters Platform S is p t k = e F( r 0 r 2 + 1 r 2 E " ln d t j;S d t j;NS x t k ;W t ; P t # + r 1 r 2 x t k ) 8k= 1;:::K (2.19) where the function e F(x) is defined as follows: e F(x) Pr(q x)= F( ¯ q)F(x) F( ¯ q)F(q) 36 . And the equilibrium choices of all types of sellers can be summarized as the following equation P t = 2 6 6 6 6 6 6 6 6 6 6 6 6 6 6 4 F( ¯ q)F(E(d t 1;S d t 1;NS jx t 1 ;W t ; P t ) 1 r 2 r 0 r 2 x t 1 r 1 r 2 ) F( ¯ q)F(q) ::: F( ¯ q)F(E(d t k;S d t k;NS jx t k ;W t ; P t ) 1 r 2 r 0 r 2 x t k r 1 r 2 ) F( ¯ q)F(q) ::: F( ¯ q)F(E(d t K;S d t K;NS jx t K ;W t ; P t ) 1 r 2 r 0 r 2 x t K r 1 r 2 ) F( ¯ q)F(q) 3 7 7 7 7 7 7 7 7 7 7 7 7 7 7 5 Y(P t ;W t ;[a;b;g;l] 0 ;[r 0 ;r 1 ;r 2 ] 0 ) (2.20) . According to (2.20), the equilibrium conjecture P t is a fixed point, which satisfies the mapping from a seller’s belief of its competitors’ entry decisions to its competitors’ beliefs of the seller’s decision. The existence of P t can be directly proved by the Brouwer Fixed Point Theorem. 2.3.3 Estimation Strategy In this simultaneous entry game, the seller’s location choice involves two sets of parameters Q= [a;b;g;l] 0 ;[r 0 ;r 1 ;r 2 ] 0 . The first set of parameters [a;b;g;l] 0 captures the consumer’s preferences and deter- mines the demand function. And [r 0 ;r 1 ;r 2 ] 0 describes the seller’s responses to competi- tor’s choices and platforms’ screening policies and takes effect in the seller’s entry cost 37 function. The estimation of Q is carried out using the Nested Pseudo Likelihood (NPL) estimator proposed by Aguirregabiria and Mira (2007). The estimation procedures are pre- sented as follows. Step 1. Estimation of[a;b;g;l] 0 I start the estimation by making an initial guess of the sellers’ strategies: ˆ P t;0 = n p t;0 k : k2f1;:::Kg o . According to Aguirregabiria and Mira (2007), this guess needs not to be a consistent estimator of sellers’ equilibrium strategies, ˆ P t = p t k : k2f1;:::Kg . Using ˆ P t;0 , I can construct the consumer’s perceptions of unobservable quality E h q t j jx t j ; m i according to (2.17) and (2.18), and write down the demand function of seller j on platform m: d t j;m in (2.11). In order to simplify the estimation, I transfer d t j;m to a lin- ear function by taking the log-difference between d t j;m and the market share of the outside option, d t 0 . lnd t j;m lnd t 0 = ax t j +E q j x t j ;m b+ price t j g + ln å j 0 2J t (m) exp h x t j 0a+E h q t j 0jx t j 0; m i b+ price t j 0g i ! (l 1) (2.21) where d t 0 is the number of consumers who choose the outside option. Calculating d t 0 requires the information of total number of potential consumers in the whole market, which 38 is usually not available in the data. To deal with this problem, I follow the previous litera- ture and assume a fixed number of potential consumers for product t. I estimate[a;b;g;l] 0 by minimizing the distance between market shares predicted by the model and those observed in the data. [ ˆ a 1 ; ˆ b 1 ; ˆ g 1 ; ˆ l 1 ] 0 = argmin å t å j lnd t j;m lnd t j;m 2 where lnd t j;m is the market share observed in the data. Step 2. Estimation of[r 0 ;r 1 ;r 2 ] 0 Given P t;0 and the estimator[ ˆ a 1 ; ˆ b 1 ; ˆ g 1 ; ˆ l 1 ] 0 , the difference of seller j’s expected profits on the two platforms can be expressed as E h 4p t;1 j X t j ;W t ; P t;0 i = E h ln ˆ d t;1 j;S ln ˆ d t;1 j;NS X t j ;W t ; P t;0 i + r 0 +r 1 X t j +r 2 q where the difference of the expected demands are determined by E h ln ˆ d t j;S ln ˆ d t j;NS X t j ;W t ; P t;0 i = E " ln å j 0 2J t (S) exp ˆ u t j 0 ;S ! ln å j 0 2J t (NS) exp ˆ u t j 0 ;NS ! jX t j ;W t ; P t # ( ˆ l 1 1) + E q t j X t j ; m= S E q t j X t j ; m= NS ˆ b 1 and a consumer’s utility from seller j 0 on platform m predicted by the estimator[ ˆ a 1 ; ˆ b 1 ; ˆ g 1 ] 0 equals to u t;1 j 0 ;m = x t j 0 ˆ a 1 +E h q t j 0jx t j 0; m i ˆ b 1 + price t j 0 ˆ g 1 39 . Therefore, the probability that a seller of quality type x k chooses Platform S equals to p t k = e F( r 0 r 2 + 1 r 2 E " ln ˆ d t;1 j;S ˆ d t;1 j;NS x t k ;W t ; P t # + r 1 r 2 x t k ) 8k= 1;:::K . The estimator ˆ r 1 0 ; ˆ r 1 1 ; ˆ r 1 2 0 are obtained by maximizing the likelihood of all sellers’ choices observed in the data: ˆ r 1 0 ; ˆ r 1 1 ; ˆ r 1 2 0 = argmax T Õ t=1 K Õ k=1 p t k N t k;S 1 p t k N t k N t k;S where N t k : k= 1;:::;K is the number of sellers of type fx k : k= 1;:::;Kg. n N t k;S : k= 1;:::;K o denotes the number of sellers that join Platform S. Both are observable in the data. Step 3. Fixed-Point Algorithm Using ˆ P t;0 and estimators[ ˆ a 1 ; ˆ b 1 ; ˆ g 1 ; ˆ l 1 ] 0 and ˆ r 1 0 ; ˆ r 1 1 ; ˆ r 1 2 0 , we can calculate the entry probability vector, ˆ P t;1 , specified in 2.20: ˆ P t;1 =Y ˆ P t;0 ;W t ;[ ˆ a 1 ; ˆ b 1 ; ˆ g 1 ; ˆ l 1 ] 0 ; ˆ r 1 0 ; ˆ r 1 1 ; ˆ r 1 2 0 . If the distance between ˆ P t;1 and ˆ P t;0 is very small such that k ˆ P t;1 ˆ P t;0 k c 0 where c 0 is a small positive number near zero, it means that the seller’s equilibrium strategy generated from ˆ P t;0 coincides with its competitors’ conjecture of the seller’s strategy. In 40 other words, ˆ P t;0 is the fixed point that satisfies the mapping defined by (2.20) and the equilibrium solution of the game is obtained. Ifk ˆ P t;1 ˆ P t;0 k c 0 , the estimation continues. I replace ˆ P t;0 with ˆ P t;1 and repeat Step 1 and Step 2 to get[ ˆ a 2 ; ˆ b 2 ; ˆ g 2 ; ˆ l 2 ] 0 and ˆ P t;2 ... and keep the iteration until ˆ P t;R1 converges, that is ˆ P t;R =Y( ˆ P t;R1 ;data;[ ˆ a R1 ; ˆ b R1 ; ˆ g R1 ; ˆ l R1 ] 0 ; ˆ r R1 0 ; ˆ r R1 1 ; ˆ r R1 2 0 ) and k ˆ P t;R ˆ P t;R1 k c 0 . In this case, ˆ P t;R1 is the vector of sellers’ equilibrium strategies and the estimators [ ˆ a R1 ; ˆ b R1 ; ˆ g R1 ; ˆ l R1 ] 0 and ˆ r R1 0 ; ˆ r R1 1 ; ˆ r R1 2 0 are the parameters which best describe the observed consumers’ and sellers’ decisions. 2.4 Data and Estimation Results 2.4.1 Background In section 4, I apply the structural simultaneous entry game specified in Section 3 to the data of Alibaba. In this subsection, I first introduce the background of Alibaba and its business strategy and then discuss the data. The Alibaba Group, a Chinese firm which operates online trading platforms, has seized a leadership position in the worldwide fast-growing E-commerce market. According to 41 the financial report from Alibaba, the gross merchandise value processed on Alibaba’s platforms in 2013 is $248 billion, exceeding that of Amazon ($116.4 billion) and eBay ($85.7 billion) combined. The company also outpaces their American counterparts in terms of the profit margin and the growth of annual revenue. As for the market size, Alibaba operates the largest online trading platforms in the world. As of 2013, Alibaba’s platforms had hosted more than 7 million merchants selling various products. On the consumer side, there were 231 million active users across Alibaba’s platforms and each active user made 49 purchases during that year, according to Alibaba. To better serve sellers and consumers, Alibaba divides its marketplace into two shop- ping sites: Tmall and Taobao and implements differentiated quality management strategies on the two platforms. To be specific, Taobao is a free-to-entry market which neither screens the products nor charges sellers any transaction fees unless sellers want to use the services like advertisements and the payment system. Compared to Taobao, Tmall has a rigorous control of the quality of products sold on the platform. First, Tmall targets sellers which are brand owners or the retailers that are officially registered with China Department of Administration for Industry and Commerce. A merchant must submit the registration cer- tificate and other related legal documents in order to qualify for entering Tmall. Second, Tmall may ask a seller to provide sample products for quality examination. Most of all, Tmall requires each seller to maintain a deposit in an account accessible by Tmall. Once Tmall finds a seller to sell products of inferior quality, it has the right to punish the seller and confiscate part of the deposit, which can be amounted as much as five times of the transaction value of the product. If the seller wants to continue its business on Tmall, it 42 has to refill the deposit to the original number. This policy makes a seller’s profit positively correlated with the quality of product. Although Tmall and Taobao perform different quality controls, they share some features on the settings of their online markets: On the design of the seller’s webpage, they adopt a uniform framework, based on which individual sellers can add descriptive introductions of products and upload product pictures. Both platforms provide rating systems through which consumers can rate the products, and publish the rating statistics on the seller’s webpage. To coordinate sellers’ participation, on one hand, Alibaba requires sellers to be single-homing which means a seller cannot simultaneously do business on Tmall and Taobao. On the other hand, Alibaba offers sellers the flexibility of transferring across the two markets over time. A merchant can initiate a transfer application anytime and move to the other platform as long as its application is approved by Alibaba. The seller’s historical data including past sales, rating scores, payment records, product descriptions also gets re-posted on the new site. According to above descriptions, it is easy to find that Tmall and Taobao are exactly counterparts of Platform S and Platform NS in my model. Both platforms are operated by Alibaba but have different quality screening standards. Tmall screens sellers’ products for quality. While on Taobao, there is no quality regulation. Alibaba requires sellers to be single-homing but allows them to transfer across two markets without losing any historical records. These business strategies fairly match the setups of my theoretical model and provide a good context to empirically study the impact of platform screening on the choices of consumers and sellers. 43 The size and business strategy of Alibaba make it an attractive data source for me to conduct the empirical study. I first develop a web-crawling program using Python and Perl to collect data from Tmall and Taobao. This data is a seller-level cross section dataset about 89 camera models sold on the two sites in July 2014. It contains each individual seller’s information including camera ID, the platform the seller is located on (Tmall or Taobao), price, sales within the past 30 days, rating scores. The definitions of these variables are presented as following. Camera ID: each camera model is treated as an independent product. For example, Nikon D3300 is one product and Canon 500D is another. The variable of camera ID helps to identify all sellers of a particular camera. Sales within the past 30 days: This variable records the number of cameras sold by a seller in the past month. Every time a seller receives an order, the system updates the seller’s sales information and publishes it on the seller’s webpage. This variable will later be used to construct the seller’s market share. Rating score: Both Tmall and Taobao allow buyers to rate sellers and their products using three criteria: whether the item was as described, the shipping and return speed, and customer service. For each criterion, a buyer can submit a score ranging from 0 to 5. Using the scores from all previous buyers, the system calculates the average score for each of the three criteria and posts them on the seller’s webpage for the review of future buyers. Several features of the rating scores need to be mentioned: First, in the course of calculation, the system does not distinguish the category of products. So the statistics not just represent consumers’ feedbacks about a particular camera model, but reflect the average quality of all kinds of products sold by the seller. Second, compared to the sales data which gets 44 updated immediately after orders are placed, the update of rating has a significant time delay. This is because the system has to wait for the feedback from consumers. Suppose a consumer purchases a Nikon D3300. The sales of this camera are immediately increased by 1. But it may take several days for the consumer to receive the product. When the consumer tries the product and posts the rating, additional one or two weeks may have passed. So the consumer’s rating associated with this transaction could arrive to the platform’s database three or four weeks later than the sales information. The rating scores, although informative of the seller’s reliability, only reflect partial information about quality. First, as mentioned above, the rating score can come from buy- ers’ feedbacks on any product sold by the seller. Given a seller may carry multiple types of products, the rating score does not necessarily demonstrate the quality of a particular product. Second, according to the policy of Tmall and Taobao, a buyer needs to submit his review with 15 days after he receives the product. It means that the rating score only reveals the consumer’s experience in a very short time period. For durable products such as cameras, two-week is a too short time for consumers to tell the overall quality. Based on these reasons, the variable of rating score can serve as a proxy of the observable quality of the product. In the estimation, I use the score of “whether the item was as described” as seller’s observable characteristic. Price: It represents the camera’s listed price. Within a month, a camera may be traded in different prices. But given the fact that there is not holiday in the month when the data was collected, the cameras’ prices should not have a large variation. Platform: This variable records the platform where the seller is located. It is a discrete variable and either equals to Tmall or Taobao. 45 Table 2.1: Variable Statistics 89 Camera Models Mean s Min Max N Number of Sellers 558.88 285.6 101 1272 35384 Rating 4.61 1.15 0 5 35384 Prices (RMB) 8405.12 7803.58 1101 99999 35384 Tmall (0/1) .0986 .2982 0 1 35384 Monthly Sales 2.19 21.09 0 1220 35384 Positive Sales (0/1) .1284 .3345 0 1 35384 Market Share .00125 .00975 0 .466 35384 Notes: Market share is defined as seller j’s sales of camera t 10;000 under the assumption that in the data period there are 10,000 potential consumers for each camera model. The variable of positive sales is a dummy which indicates whether the seller has non-zero sales. In the context of Alibaba, the entry game in Section 3 can be briefly rephrased as fol- lowing: At the beginning of a month, sellers located on Tmall and Taobao simultaneously decide whether to stay in the current platform or move to the other platform. Each seller makes decision based on the observable quality: rating scores, the private quality infor- mation and the expectation of other sellers’ location choices. At the end of the month, the web-crawling program is run to collect the seller’s choice of platform, monthly sales, prices and ratings. 2.4.2 Data Description The statistics of variables are presented in Table 1. The dataset includes 35384 observations of sellers for 89 camera models. The number of sellers for a camera varies from 101 to 1272. The average number of seller of a camera model is 559 with a standard deviation 285. Each merchant on average sells 2 units of cameras in the month of July 2014 and has a small market share: 0:125%. These evidences support my model’s assumption: A lot 46 Table 2.2: Comparisons between Tmall and Taobao Variable: Prices Mean s Min Max N Tmall 8044 6857 2080 51479 3492 Taobao 8444 7899 1 99999 31892 Variable: Individual Sales Mean s Min Max N Tmall 4.61 23.14 0 389 3492 Taobao 2.08 20.98 1 1220 31892 Variable: Positive Sales (0/1) Mean s Min Max N Tmall .2860 41.10 0 1 3492 Taobao .1210 .3261 0 1 31892 Variable: Individual Market Share Mean s Min Max N Tmall .002572 .01171 0 .3240 3492 Taobao .001114 .0095 0 .4667 31892 Variable: Total Sales on the Platform Mean s Min Max N Tmall 383.8 430.3 2 1815 89 Taobao 1200.3 1628.8 5 7696 89 Notes: The first four tables show the statistics of variables of individual sellers located on Tmall and Taobao. The last table presents the statistics of the total sales of the 89 camera models on Tmall and Taobao. of sellers compete in the market and each has a small market power. A dummy variable named positive sales is created to indicate whether a seller’s monthly sales are zero. And about 12:84% of sellers have positive sales during the data period. The average price of cameras is 8405 RMB (about 1400 dollars). There are about 10% of sellers located on Tmall. The rating score about ”whether the item was as described” has a mean 4:6 out of 5 and a standard variation 1:15. 47 In Table 2, I compare the characteristics of sellers located on Tmall and Taobao. Firstly, the average prices on Tmall and Taobao are very close, which equal to 8044 and 8444 RMB respectively. The price distributions on the two platforms are displayed in Figure 1. Most cameras sold on both platforms are priced less than 30;000 RMB. Particularly, cameras priced between 5;000 and 15;000 RMB have a big population on the two mar- kets. These cameras are usually low-end or medium-end models which target ordinary consumers instead of a small group of professional users like photographers. This guar- antees the two-sided market model specified in Section 2 can be applied to the dataset. Then I look at the sales on two platforms. The average monthly sales of a Tmall seller is 4, twice more than that of a Taobao seller: 2:08. About 28:6 percent of Tmall sellers are able to sell one or more cameras whiles this percentage falls to 12:1 on Taobao. As for the market shares of individual sellers, sellers on both platforms generally have very small market shares, although Tmall sellers have a slightly larger average market share :2572% compared to :1114% for Taobao sellers. Although on individual level, a Tmall seller per- forms better on than its peers on Taobao, the total number sales processed on Tmall is 25 percent of those on Taobao. Rating score and distribution. The variable of rating score serves as the seller’s observable quality in the estimation. It is one of the most important explanatory variables and deserves further statistical analysis. For each platform, I calculate the proportion of sellers with particular rating scores and show the results in Figure 2. The distributions of the rating score on Tmall and Taobao exhibit different trends. On Tmall, most rating scores fall into the range from 4:7 to 4:9. The distribution of rating reaches the peak at the value 48 Figure 2.1: The Distribution of Prices on Tmall and Taobao 0 5.0e-05 1.0e-04 1.5e-04 Density 0 10000 20000 30000 40000 50000 60000 70000 80000 90000 100000 prices The Prcie Distribution on Taobao Notes: The figure on the left displays the distribution of prices on Tmall; The right figure shows the distri- bution of prices on Taobao; The x-axis is the value of prices and the y-axis represents the density of prices. 4:8. There are only very small numbers of sellers located on the two tails of the line. While on Taobao, sellers’ ratings are distributed much evener along the line. Figure 3 displays the proportion of Tmall sellers in each rating score group. As the rating increases, the proportion of Tmall sellers first increases then decreases. This obser- vation is consistent with the prediction of Proposition 2.2: when the observable quality increases, the seller’s inventive to participate in Platform S (Tmall in our case) may take an inverted-U curve. To facilitate the analysis, I classify the rating scores into three groups and create a dummy variable to denote the group the seller belongs to. The rating group dummy is defined as follows: Group_1 stands for the group of sellers whose rating scores are less than 4:7; Group_2 sellers are those who have rating scores equal or larger than 4:7 but smaller than 4:9; The sellers obtaining rating scores equal or larger than 4:9 are classified to Group_3. 49 Figure 2.2: The Distribution of Rating Score on Tmall and Taobao 0 .2 .4 .6 PDF of Rating 0 1 3 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5 Rating Score Distribution on Tmall and Taobao Taobao Tmall Notes: The figure displays the distribution of sellers’ rating scores by platform. The x axis is the rating score. The blue bar stands for the proportion of sellers with corresponding rating score in the population of Taobao. The red bars present the distribution of the rating score for sellers located on Tmall. In Table 3, I present the number of sellers and the proportion of Tmall sellers in each rating group. Group_1 sellers are of a relatively small number: 3785, about 11% of the total population. The number of Group_2 and Group_ 3 are 15;620 and 15;979 perceptively. In Group_1, about 12% of sellers participate in Tmall. This proportion increases to 18% in Group_2 and then drops to 1% in Group_3. Again, this non-monotonic relationship between the rating score and sellers’ participation of Tmall coincides with the prediction of Proposition 2.2. Table 4 compares the sellers’ characteristics by rating groups and by platforms. The average price of cameras sold on Tmall increases with the rating, while on Taobao the sellers who have a medium rating charge the lowest average price. Fixing the rating group, 50 Figure 2.3: Sellers’ Choices of Platforms, By Rating Score Notes: This figure displays sellers’ entry decisions by the rating score. The x-axis is the rating score. For each value of rating score, the blue bar represents the proportion of sellers that choose Taobao, and the red bar displays the proportion of sellers on Tmall. the average prices on the two platforms are slightly different. Sellers in Group_2 and Group_3 charge a higher average price on Tmall than that on Taobao. The reverse is true for the Group_1 sellers. The second sub-table compares the monthly sales. On Tmall, Group_2 sellers acquire the largest monthly sales. In contrast, on Taobao, Group_3 sellers obtain monthly sales of 2:5 cameras, higher than that of Group_1 and Group_2: 0:04 and 1:5. This implies that consumers on Tmall and Taobao have different responses to the rating when they make purchases since the quality screening by Tmall alters consumers’ belief of the product quality. 51 Table 2.3: The Proportion of Tmall Sellers, By Rating Group Group of Rating Score Group_1 [0 4:7) Group_2 [4:7 4:9) Group_3 [4:9 5:0] Rating Score Tmall Sellers (%) 12.13 18.35 1.03 N 3,785 15,620 15,979 Notes: The sellers are classified into three groups by the rating score: Group_1 is composed by sellers with rating scores less than 4.7; Group_2 sellers have rating scores between 4.7 and 4.9 and Group_3 sellers’ rating scores are equal or larger than 4.9. This table presents the proportion of Tmall sellers and the number of observations in each rating group. 2.4.3 Estimation Results Table 5 presents the estimation results. There are two sets of parameters. The parameters in the demand function measure the consumer’s responses to the seller’s and the platform’s characteristics. The second set of parameters account for the impacts of factors playing a role in the seller’s profit function. These parameters are estimated under the assumption that there are 10;000 potential consumers for each camera model. The dummy variable of seller rating is used as the observable quality. The unobserved quality, q, is assumed to follow standard truncated normal distribution bounded on[50;50]. All estimators are of theoretically anticipated signs and statistically significant. A seller that has a higher rating score acquires a larger market share. If a seller manages to raise his rating score from Group_1 (less than 4:7) to Group_2 (between 4:7 and 4:9), his (log) market share can increase by 3:05. Similarly, the sellers in Group_3 obtain a market share 2:46 bigger than that of Group 1. The price, as expected, has a negative effect on sales. An increase of 1;000 RMB on a camera’s price leads to a 0:051 loss of the market share. 52 Table 2.4: Comparisons between Tmall and Taobao, By Rating Group Prices Tmall Taobao Mean s Min Max Mean s Min Max Rating Group_1 7870.1 7072.9 2080 48688 8401.2 7634.1 1 88888 Rating Group_2 8015.6 6717.1 1120 51479 7887.4 7476.4 1120 99999 Rating Group_3 9072.1 8446.1 2398 49000 8903.1 8249.8 499 99999 Individual Monthly Sales Tmall Taobao Mean s Min Max Mean s Min Max Rating Group_1 1.113 3.482 0 38 .04239 .5101 0 25 Rating Group_2 5.552 26.759 0 393 1.592 14.83 0 677 Rating Group_3 .6667 3.628 0 29 2.579 26.16 0 1220 Positive Sales (0/1) Tmall Taobao Mean s Min Max Mean s Min Max Rating Group_1 .2527 .4350 0 1 .02585 .1587 0 1 Rating Group_2 .3017 .4591 0 1 .1394 .3464 0 1 Rating Group_3 .1212 .3274 0 1 .1061 .3079 0 1 Individual Market Share Tmall Taobao Mean s Min Max Mean s Min Max Rating Group_1 .001449 .007286 0 .1042 .0001405 .001840 0 .07143 Rating Group_2 .002885 .01256 0 .3241 .001234 .008414 0 .3333 Rating Group_3 .0002654 .001202 0 .007576 .001221 .01113 0 .4667 According to the theory, consumers update their belief of the seller’s private quality according to the seller’s rating and choice of platform, and take the belief into account when they choose among sellers. This screening effect, in the empirical study, is captured by the parameters ofE[qjX;m]. In order to investigate the impacts of quality screening on the profits of sellers that belong to different rating groups, I construct an intersection terms usingE[qjX;m] and the rating group dummy, and estimate their parameters. These estimators vary by the seller type. More specifically, for Group_1 sellers, the parameter of 53 E[qjX;m] is 2:59, which suggests a strong screening effect. By joining Tmall, this type of sellers can improve consumers’ expectation about the product quality and obtain a larger market share. As for the Group_2 sellers, this estimator slightly decreases by 0:77, but still remains positive and significant. It indicates the screening effect also plays a role here. For Group_3 sellers that have the highest rating score, the impact of E[qjX;m] is 2:59 minus 2:86, which is negative and almost zero. This means the screening effect disappears and joining Tmall does not help these sellers to prompt sales. These estimations of the parameters ofE[qjX;m] are consistent with Proposition 2.1: when the observable quality is lower than certain threshold, joining Platform S can help sellers to signal their quality and increase the sales. But this screening effect vanishes if the observable quality is sufficiently high such that sellers can always pass the screening. Besides the screening effect, the network and competition effects also influence a seller’s market share. The theory in Section 2 shows that, when a platform hosts more sellers of good quality and provides higher total expected utility to consumers, an individ- ual seller can become better or worse, depending on whether the network effect dominates the competition effect. The relative magnitude of the network and competition effects is captured by (l 1), the parameter in front of lnEU m . Table 5 shows that this parameter is positive, suggesting that the network effect plays a dominant role on Tmall and Taobao. When the total expected utility offered by the entire group increases by 1, an individual seller’s (log) market share enlarges by 1:71. A seller’s choice of platform is governed by the expected demands on two platforms and the seller own quality types. The parameters of these variables are reported in the second 54 part of Table 5. The parameter ofE[ln d j;S d j;NS ] equals to 0:62, which is positive and significant. This implies that a seller is more willing to join Tmall if it expects to enjoy a larger market share on Tmall. Moreover, if we recall the seller’s entry probabilities specified in (2.16), the parameter ofE[ln d j;S d j;NS ] also characterizes the impact of the unobservable quality on a seller’s comparative profit on Tmall. The estimation result indicates this impact is positive, which is coherent with the theory. The coefficients of Group_2 and Group_3 are respec- tively 1:296 and 2:333, which suggests that a seller’s relative profit on Tmall increases with the rating score. This is also consistent with the spirit of the quality screening: a seller of higher observable quality pays less cost of screening. Using the estimators in Table 5, I obtain the sellers’ choice probabilities predicted by the model. To test the model’s prediction power, I compare the predicted probabilities with sellers’ choices observed in the data, and measure their differences with a variable: prediction error. Figure 4 displays the statistics and distribution of the prediction errors. The prediction errors have an almost zero average3:37 10 6 and a maximum 0:209 and minimum0:376. This means that on average the predicted choice probabilities do not deviate too much from the observed data. About 33% prediction errors fall into a small interval of length 0:005 covering point zero. It suggests for these sellers, the model well predicts their choices. Over two thirds of prediction errors have absolute values less than 0:05. Some prediction errors are large but their densities are very small in the whole population. Overall, the sellers’ choices of platform are well explained by the models in Section 2 and Section 3. 55 Figure 2.4: Distribution of Prediction Errors, Sellers’ Choice Probabilities Notes: The prediction error is defined as the difference between the seller’s choice probability predicted by the model and the probability observed in the data. The statistics of prediction errors are presented at the bottom of the figure. Counterfactual Analysis. The estimation results show that quality screening employed by Tmall plays an important role in determining the consumer’s utility and seller’s profits on the two platforms. It further influences the consumer’s demand of platforms and sellers, and the seller’s choices of platforms. This is important for Alibaba, the parent firm of Tmall and Taobao, which derives its profit mainly from the transactions processed in the two marketplaces. According to the theoretical model, the transaction volume on Alibaba depends on the number of consumers that patronize Tmall and Taobao. Fixing the utility provided by the outside option, if Alibaba alters the screening policy of Tmall, it can be expected that the consumer’s demand for Tmall and Taobao also changes. To quantify the impact of screening on Alibaba’s business, I conduct a counterfactual analysis in which I assume Alibaba cancels the screening policy and makes Tmall a free-entry market. 56 If Tmall becomes a free-to-enter market, it would have no difference from Taobao. So the case is the same as that if Alibaba only operates one platform: Taobao. Consumers choose either Taobao or the outside option depending on which provides a higher utility. Suppose all sellers continue to run their business in the same product market as before, now they have no options but to participate in Taobao. Since there is no screening effect, the consumer’s expectation of a seller’s unobservable quality equals to the population mean: E(q)= 0. Therefore, the consumer i’s utility from purchasing seller j is reduced to ˜ u t i; j = u t i; j +e t i; j = x t j a+ price t j g+e t i; j , in which the impact of the seller’s unobservable quality vanishes. Figuring out the utility consumers obtain from an individual seller, now we can com- pute the consumer’s expected utility from Alibaba’s platform(s) before and after Alibaba would remove quality screening. But before that, there is one problem we needs to pay attention: I have characterized the consumer’s choice using a Multinomial Logit model. It is well known that for this type of models, if two alternatives are merged into one, the number of consumers that choose the new alternative must decrease. This fact holds even if the characteristics of the two alternatives remain the same before and after merger. Related to our case, suppose Alibaba merges Tmall and Taobao into one platform but still imposes quality screening on Tmall sellers, there will be fewer consumers visiting the merged plat- form. This change is not due to quality screening but only because we reduce the choice 57 set of consumers from three options (Tmall, Taobao and the outside option) to two options (merged platform and the outside option). In order to fairly investigate the effect of quality screening, I construct the follow- ing variable to compare the change of consumers’ utility before and after Alibaba would remove quality screening: CU t = å m2fS;NSg å j 0 2J t (m) exp h x t j 0 a+E h q t j 0 jx t j 0 ; m i b+ price t j 0 g i å all j of product t exp h X t j a+ price t j g i . The numerator captures the total utility provided by all sellers of product t, when Alibaba employs quality screening to discriminate sellers. This number can also be understood as the proportion of consumers visiting sellers located on Alibaba compared to the proportion of consumers that choose the outside option. The denominator measures the total utility offered by sellers if there is no quality screening. Table 2.6: Counterfactual: Change of Consumer Utility Mean s Min Max N (camera models) CU 2.86 1.89 .562 7.99 89 1(CU > 1) .742 .441 0 1 89 Notes: The variable CU is defined as the ratio of total utility that sellers provide to consumers before and after Alibaba would remove the quality screening on Tmall. The number of camera models in the data is 89. If this ratio is bigger than one, it means the quality screening policy improves con- sumers’ welfare, and to some extent also helps Alibaba to achieve a better position in the 58 competition with the outside option. In Table 6, I present the statistics of CU. The variable CU of the 89 camera models has a mean of 2:86, which suggests consumers can enjoy larger utility from sellers when Alibaba screens products for quality. For 74% camera models, CU takes values larger than one, which indicates the quality screening alleviates the problem of asymmetric information, benefits consumers, and also prompts Alibaba’s market share. 2.5 Conclusion In two-sided markets, a user’s utility depends not only on the number of users on the other side, but also the quality provided by the other side. Previous studies of two-sided markets have mainly focused on the quantity externality. Less attention has been paid to end-users’ concerns about quality. In this paper I propose a model which incorporates both quality and quantity in the end-users’ interactions, and analyze how platforms can use quality screening to alleviate the problem of asymmetric information and motivate end-users’ participation. I study this question from both the theoretical and empirical perspective. First, I build a theory in which sellers compete for selling a particular product to con- sumers through online trading platforms. The product quality is heterogeneous and imper- fectly observable to other players other than the seller itself. I model duopoly platform competition where one platform (Platform S) uses quality screen and the other (Platform NS) does not. I show that the quality screening influences the consumer’s belief of the qual- ity and the choice of sellers and platforms. These choices result in the screening, network and competition effects in turn drive sellers to different platforms. 59 Next, I formalize the end-users’ choices in the theory as a simultaneous entry game with incomplete information, and carry out the estimation using the data from Alibaba’s Tmall and Taobao. The estimation results are consistent with theory: the screening effect varies by the observable quality, and the screening cost decreases with quality. Moreover, I find the network effect overrides the competition effect in the case of Alibaba. Do birds of a feather flock together? Not necessarily. The comparative statics illustrates that under the influence of the screening effect, the seller’s incentive to submit to quality screening first increases with the observable quality. Once the observable quality reaches a certain point, the network and competition effects take over and may drive sellers to the platform which does not use screening. In other words, the seller of high observable quality may be willing to pool with the seller with low observable quality, in order to enjoy the network effect or avoid the competition effect. In this sense, the birds of a feather do not always flock together. Does the quality screening benefit consumers and the platform provider? Yes. Using the estimation results, I conduct the counterfactual analysis and study the change of the consumers’ utility if Alibaba did not employ quality screening. I find that with the presence of quality screening, the total utility that consumers obtain from the entire seller group gets increased in 70% of camera markets in the data. Quality screening helps Alibaba to attract more consumers and increases its market share. 60 Table 2.5: Estimation Results Coefficients (Std. Error) Variables of Demand Function Rating Group_2 3:049 (0:0710) Rating Group_3 1:583 (0:0089) Price ( 1000 RMB) 0:0514 (0:0181) E(qjX;m) 2:598 (0:0334) Rating Group_2*E(qjX;m) 0:7712 (0:0316) Rating Group_3*E(qjX;m) 2:863 (0:0501) lnEU m 1:714 (0:0601) Constant 19:27 (0:49) Variables in Entry Function E h ln d j;S d j;NS i 0:6179 (0:0387) Rating Group_2 1:296 (0:0547) Rating Group_3 2:333 (0:0184) Constant 4:821 (0:1667) Notes: Standard errors are in parentheses. * p < 0.1; ** p < 0.05; *** p < 0.01. E(qjX;m) stands for the consumer’s expectation of q conditional on the seller’s observable rating score, X and the platform m on which the sellers is located. EU m is the consumer’s expected maximum utility from platform m. d j;m is seller j’s market share on platform m. 61 Chapter 3 Optimal Screening Standard 3.1 Introduction In this chapter, I discuss the platform’s optimal choice of screening standard. To understand this issue, I build a model which extends the traditional two-sided market models (Rochet and Tirole (2003, 2006); Armstrong (2006)) in threefold: first it captures the consumer’s concern of quality when they evaluate the utility from the seller side. Second, it derives the consumer’s and seller’s equilibrium reactions to the quality screening. Third, it analyzes the optimal quality screening for the consumers and the platform. I consider a platform through which consumers can get access to content “products” like blogs, columns or academic articles by independent “sellers” such as bloggers, colum- nists or researchers. I assume consumers have homogenous preference for the quality and purchase a product as long as they believe its quality is higher than the consumer’s reser- vation value. The products are of heterogeneous quality, which information is imperfectly observable to consumers. The platform can choose to implement quality screening and select qualified products onto the market. Consumers and sellers observe the platform’s screening policy, and simultaneously decide whether to participation in the platform and whether to trade with each other. 62 I first analyze the choices of consumers and sellers before and after the platform uses quality screening. Without screening, the platform is a free-entry market, and consumers formulate the belief of quality solely according to the observable characteristics of the prod- uct. In equilibrium, consumers only choose the products with sufficiently high observable signals. Those products of good total quality but low observables are mistakenly neglected by consumers and forced to exit the market, which results in an efficiency loss. This situa- tion, however can get alleviated when the platform implements quality screening. Quality screening enriches the consumer’s information set: when a product is selected by the plat- form, the consumer knows not only its observable signal but also that its total quality is higher than the standard set by the platform. Therefore, the products of good total quality, even if they may have unfavorable observables, have a chance to sell and are motivated to enter the market. As the screening standard varies, there could exist either a pooling or separating equilibrium for the sellers’ decision of entering the platform. Then I investigate the quality screening standards which maximize consumers’ welfare and the platform’s profit. I show that the consumers’ welfare achieves its maximum when the screening standard equals to the consumer’s reservation value, while the platform finds it optimal to set the standard below the reservation value in order to attract more products on board. This is consistent with the findings in previous literature: the operator of a two-sided market needs to coordinate the participation on both sides for its profit maximization. I also find that compared with the case in which the platform directly tells consumers about the products’ true quality, the platform can profit more by just informing consumers whether the product’s quality has exceeded a quality threshold or not. 63 The rest of the product is organized as follows: Section 2 presents the model settings, including the player’s characteristics and the sequence of the game. In Section 3, I first analyze the equilibrium choices of consumers and sellers when the platform screens the product, and compare the results to the case of no screening. Then I derive the optimal screening standards for consumers and platforms. I also discuss different ways that the platform can do the screening and their profit implications. The last section is the conclu- sion. 3.2 Model Setup This section introduces the characteristics of the players involved in the game. 3.2.1 Heterogeneous Sellers Without loss of generality, we assume that the number of sellers is of measure 1. Each seller has only one type of products for sale. We denote the quality of the product sold by seller j as q j , which is composed of three parts: q j =m j +q j +e j , where m j is the observable quality of the product. Taking academic articles for example, m j can be the the article’s title, the topic it covers, and the author’s reputation such as her professional title, academic affiliation, previous studies and publications. u j is fixed and perfectly observed by all players. The second component,q j , represents the seller’s private 64 information about the quality of the product. q j is observable only by seller j unless the product is screened by the platform. Back to the previous example, q j can be understood as the content of the article, the methodology it utilizes and the robustness of the results. e j denotes the part of quality which is revealed during the screening. It could be the revisions requests from the referees which also influences the article’s final quality. The platform could learn q and e if it screens the product. m; q and e are drawn from distributions whose properties are common knowledge and satisfy Assumption 3.1. Assumption 3.1: The distributions ofm,q ande satisfy: (i). m,q ande are independent random variables with support on(¥;+¥). (ii). m,q ande follow distributions: m f m ,q f q ande f e , where f m , f q and f e are log-concave functions. (iii). m,q ande have a mean of zero: E(m)= E(q)= E(e)= 0. We assume the support of m; q and e are unbounded such that we do not need to discuss the possible corner solutions of the model. As we have mentioned in Chapter 2 of this dissertation, the family of log-concave probability distributions is commonly used in economics. The zero-mean assumption is for normalization and can be relaxed without changing main results of this study. 3.2.2 Platform Screening The platform provides a marketplace in which sellers can trade with consumers. The plat- form can use a screening mechanism to select the products whose quality meets the require- ment. The selection proceeds as follows: The platform first announces a quality standard 65 k. Then the seller decides whether to submit entry application. Next the platform reviews the seller’s product and gets perfect information about its quality q. If and only if q k, the platform approves the seller’s entry. 3.2.3 Consumer’s Purchase Decision We assume the number of potential consumers is of measure 1. They have homogeneous preference for quality, and get utility ˜ b(m;k) from the seller: ˜ b(m;k)= E(qjm; q k) c b where E(qjm; q k) represents the consumer’s expectation about the product quality con- ditional on the observable quality m and the platform’s quality standard k. And c b denotes the consumer’s willingness to pay for each product, or the reservation value for the product. We keeps c b a constant number in the following analysis. The consumer purchases the product as long as ˜ b(m; k) 0. His total expected utility from joining the platform equals to U b (k) = Q m (k) [ ˜ b(m; k)Pr(q k;m) f(m)]dm whereQ m (k) denotes the set ofm satisfying ˜ b(m; k) 0, i.e., Q m (k) = fm s.t. ˜ b(m; k) 0g 66 . Recall that Pr(q k) is the probability that the seller passes the screening test and enters the platform. With some simple mathematics, the above conditional expectation of quality can be converted as follows: U b (k)= Q m (k) [E(q c b ;m; q k) f(m)]dm . We assume that the consumer has to pay an opportunity cost B for shopping on the platform. B is stochastic and follows a log-concave distribution F B . When the expected utility U b (k) exceeds the opportunity cost B, the participation occurs. So the total number of consumers on the platform is: N b (k)= F B (U b (k)) 3.2.4 Seller’s Profit As illustrated in previous section, only the seller with observable quality m2Q(k) can make sales. And the realized total sales equal to the total number of consumers on the other side. In other words, the seller faces a demand: D(m; k) = N b (d) 1[m2Q(k)] . We assume the seller obtains a profit margin b s from each sale. To simplify the analysis, we takes b s as exogenous given and homogeneous among sellers. For each transaction, a seller pays the platform a fee p. Besides, a constant opportunity cost t s occurs when the 67 seller joins the platform. Hence, for a seller with observable quality type m, the expected profit on the platform is: p s (m;q; p;k) = Pr(q> k)[(b s p)D(m;k)t s ] = [1 F e (kmq)][(b s p)D(m; k)t s ] . If this profit is non-negative, the seller applies for joining the platform. The measure of sellers on the platform is: N s (p; k)= 1[p s (m;q; k) 0]dF(m) 3.2.5 Platform’s Profit The platform collects a fee amount of p from the seller for each fulfilled transaction. There is no charge on consumers. The platform’s profit is the per-transaction fee times the total volume of transactions, which can be expressed as: p M (p; k)= pN b (k)N s (p; k) 3.2.6 Sequence of the Game The game proceeds in the following sequence: 68 Period0: m,q ande are randomly drawn from distributions f m , f q and f e , and jointly determine the quality of the product q= u+q+e . At this point, m is observable to all players. q is the seller’s private information. Ande remains unknown by all players. Period1: The platform announces the per-transaction price p; and its quality standard k. Consumers and sellers simultaneously make their entry decisions. Period2: Consumers interact with sellers and realize the purchases. 3.3 Equilibrium Analysis To illustrate the effects of screening on the decisions of sellers and consumers, we firstly analyze the case in which the platform does not screen products. Then we can compare it with the case with screening. 3.3.1 No Screening Proposition 3.1. If the platform doesn’t screen, there exits a separating equilibrium such that: (i) Sellers: the seller participates in the platform if the product’s observable quality satisfies m c b 69 . The number of sellers on the platform is N s = 1 F m (c b ). (ii) Consumers: the consumer joins the platform if the expected benefit from the plat- form U b;ns follows U b;ns B where U b;ns = E(m c b ;m c b ) . The number of consumers on the platform is N b;ns = F B (U b;ns ). The consumer purchases from seller with observable quality typem c b . (iii) Platform: The platform sets the per-transaction price equal to p= b s t s N b;ns and earns a profit p M =[b s F B (U b;ns )t s ][1 F m (c b )] . Proof: The case of no screening is equivalent to that the platform sets the standard to be k=¥. The consumer’s expected utility of purchasing from type-m seller is ˜ b(m; k=¥) = E(q) c b = m+ E(q)+ E(e) c b = m c b 70 , which is positive iffm c b , i.e., the consumers only visits those seller with typem c b . The consumer’s total expected utility of interacting with the sellers on the platform, therefore, can be expressed as U b;ns U b (k=¥) = E(q c b ;m c b ) = E(m c b ;m c b ) = ¥ c b (m c b )dF m . The consumer joins this platform if and only if above utility is larger than the value of outside option B. And the total number of consumers on the platform is N b;ns N b (k=¥) = Pr(U b;ns B) = F B (U b;ns ) Anticipating the consumer’s purchasing decision, only sellers that hold product signal m c b have an incentive to attend the platform and get profitsp s : p s =(b s p)N b;ns t s 71 . The measure of these sellers is N s;ns N s (k=¥) = Pr(m c b ) = 1 F m (c b ) Next, we consider the platform’s strategy. As shown in previous analysis, the platform’s profit depends on two terms: total transaction volume N b;ns N s;ns and the per-transaction fee p. Without of screening, the first term is purely determined by c b . Hence, to achieve optimization, the platform just needs to maximize p under the condition that those sellers withm c b earn non-negative profits: (b s p)N b;ns t s 0, p b s t s N b;ns . The platform’s profit is p M = pN b;ns N s;ns = (b s t s N b;ns )N b;ns N s;ns s = [b s F B (U b;ns )t s ][1 F m (c b )] Q.E.D. Without screening, the platform servers as a free-entry market and all types of sellers can post their products for sale. A product’s observable quality is the only information 72 that the consumer can utilize for inferring the product’s quality and making decisions. As shown in Figure 1, a transaction occurs only when the observable quality of the product is sufficiently high to cover the consumer’s reservation value. The products with observable quality below the reservation value cannot be sold and forced to exit the platform. Figure 3.1: The Equilibrium without Screening In this case, the consumers’ reservation value, c b , is the key factor that influences con- sumers’ demand. Its comparative statics are shown in the following lemma. Lemma 3.1. The following statistics all decrease with c b : (1) the number of consumers on the platform (2) the number of sellers on the platform (3) the profit of the platform Proof: According to Proposition 3.1, a consumer’s expected utility from the platform is U b;ns = ¥ c b (m c b )dF m 73 . It is easy to show that ¶U b;ns ¶c b = 1 F m (c b ) < 0 . Therefore, the number of consumers joining the platform decreases with c b . The same holds for the number of sellers, N s;ns = 1 F m (c b ). When the number of users on the two sides decreases, the transaction on the platform also gets shrunk, which reduces platform’s profit. Q.E.D. Lemma 3.1 shows that an increase of the reservation value can exacerbate the asym- metric problem and negatively influence all players’ benefits in equilibrium. 3.3.2 Screening In this subsection, we add the screening mechanism to the previous model and discuss the player’s equilibrium strategy in Proposition 3.2. Proposition 3.2. Suppose the monopoly platform employs and determines the quality standard to be k, where k>¥ If k c b ,thereisapoolingequilibrium (i) Sellers: all sellers apply for joining the platform and have a probability Pr(q k) to enter. Each seller earns zero profit on the platform. (ii) Consumers: the consumer joins the platform if the ex-ante expected utility from the platform satisfies U b (k) B 74 where U b (k)= E(q c b ; q k) . The number of consumers on the platform is N b (k)= F B (U b (k)). The consumer purchases from all sellers on the platform. (iii) Platform: The platform sets the per-transaction fee equal to p= b s t s N b (k) and earns a profit p M (k)=[b s F B (U b (k))t s ]Pr(q k) . The optimal standard is determined by: k = maxfc b ; max k p M (k)g If k< c b ,thereisaseparatingequilibrium. (i) Sellers Ifmm (k), the seller applies for joining the platform and has a probability Pr(q k) to enter. Each seller on the platform earns zero profit; Ifm <m (k), the seller stays out of the platform; wherem (k) is decided by the following equation m (k)+ E(q+ejq+e km (k))= c b . The number of sellers on the platform is N s (k)= Pr(q k;mm (k)). 75 (ii) Consumers: the consumer joins the platform if U b (k) B where U b (k)= E(q c b ; q k;mm (k)) . The number of consumers on the platform is N b (k)= F B (U b (k)). The consumer purchases from sellers from seller with observable quality typemm (k). (iii) Platform: the platform sets the per-transaction fee equal to p= b s t s N b (k) and earns a profit p M (k)=[b s F B (U b (k))t s ]N s (k) . The optimal screening standard is determined by: k = minfc b ; max k p M (k)g. Proof: See details in Appendix B When the monopoly platform screens seller’s products upon their entries, it changes the consumer’s information set and the expectation of quality. The consumer not only observes the signal m, but also knows that that the products selected onto the platform have total 76 (a) The Equilibrium when k c b (b) The Equilibrium when k< c b Figure 3.2: The Equilibrium with Screening quality higher than k. Based on these information, the expected utility of purchasing from type-m seller is ˜ b(m; k) = E(qjm; q k) c b . As shown in Figure 2(a), when the standard is sufficiently high to cover the consumer’s willingness to pay, i.e., k c b , ˜ b(m; k) is always positive. Consumers shop from all sellers on the platform and the observable quality becomes a redundant signal. Lemma 3.2 investigates the effect of changing the standard k on the player’s welfare in this situation. Lemma 3.2. When the standard satisfies k> c b , by lowering the quality standard, the platform owner can always increase (1) the number of consumers on the platform (2) the number of sellers on the platform 77 (2) the profit of the platform Proof: Following Proposition 3.2, the number of sellers that can pass the screening is Pr(q k), which is a decreasing function of k. A consumer’s ex-ante utility from the platform, U b (k) = E(q c b ; q k) = qk (q c b )dF(q) is also negatively correlated with k because ¶U b (k) ¶k = (k c b ) f(k) < 0 . Therefore, by reducing k, the platform is able to attract more sellers and consumers and obtain a higher profit. Q.E.D. Lemma 3.2 suggests that there is an efficiency loss when k > c b . In this case, those sellers with quality q2[c b ;k] are excluded from the platform, even if their products are worthy buying. Losing the opportunity of interacting with these good sellers, consumers have a decreased ex-ante utility on the platform. Hence, in this case, the higher the quality standard is, the more sellers and consumers the platform would lose. 78 Let’s analyze the case of k c b . Now the consumer’s expectation about a product’s quality, ˜ b(m;k), is not necessarily positive. The consumer needs to take the product’s observable qualitym into consideration when they decide whether to buy from a seller According to the assumption that m, q and e have log-concave distributions, we can show that ˜ b(m;k) is an increasing function of m and there exists a cutoff point m (d) such that ˜ b(m; k) 0 for all mm (k). The consumer, therefore, chooses only products of observable quality mm (k). The property ofm (k) is presented in the following lemma. Lemma 3.3 when k< c b ,m (k) decreases with k. Proof: Following Proposition 2,m (k) is determined by the equation m (k)+ E(q+ejq+e km (k))= c b and taking first difference with respect to k, we get m 0 (k)+¶ E(q+ejq+ekm (k)) ¶(km (k)) [1m 0 (k)] = 0 )m 0 (k)= ¶ E(q+ejq+edm (k)) ¶(dm (k)) 1¶ E(q+ejq+edm (k)) ¶(dm (k)) 79 which is negative since ¶ E(q+ejq+ekm (k)) ¶(km (k)) 2(0;1) . This is satisfied because according to Assumption 3:1,(q+e) is log-concave distributed, and for any log-concave distribution, its conditional mean is an increasing function bounded within(0;1). Q.E.D. The result in Lemma 3.3 is quite intuitive. When the platform implements a tougher screening, the consumers form a higher expectation of the quality of the products, and include those products with relatively lower observable quality into set of purchase. As the purchase set varies with the screening standard, consumers may get different ex-ante utility from the platform. Lemma 3.4 discusses the optimal standard from the consumer’s point of view. Lemma 3.4 The consumer’s welfare gets maximized when k= c b , so does the number of consumers. Proof: Let’s first work on the consumer’s welfare. As shown in Lemma 3.2, when k c b , the consumer’s welfare U b (k), is a decreasing function of k. To prove the statement in Lemma 3.4, our remaining job is to prove U b (k) increases with k when k< c b . 80 According to Proposition 3.2, when k< c b , the consumer’s ex-ante utility of shopping on the platform equals to U b (k) = E(q c b ;q k;mm (k)) = ¥ m (k) ¥ km (m+q+e c b ) f q+e (q+e)d(q+e) f m (m)dm Letn =q+e, the above function can be written as U b (k) = ¥ m (k) ¥ km (m+n c b ) f n (n)dn f m (m)dm For an arbitrary k 1 , k 2 such that k 2 < k 1 < c b , we compare the magnitude of U b (k 1 ) and U b (k 2 ) by taking the difference U b (k 2 )U b (k 1 ) = ¥ m (k 2 ) ¥ k 2 m (m+n c b ) f n (n)dn f m (m)dm ¥ m (k 1 ) ¥ k 1 m (m+n c b ) f n (n)dn f m (m)dm 81 where U b (k 2 ) can be further expressed as U(k 2 ) = ¥ m (k 2 ) ¥ k 2 m (m+n c b ) f n (n)dn f m (m)dm = ¥ m (k 2 ) " k 1 m k 2 m (m+n c b ) f n (n)dn+ ¥ k 1 m (m+n c b ) f n (n)dn # f m (m)dm = ¥ m (k 2 ) " k 1 m k 2 m (m+n c b ) f n (n)dn # f m (m)dm + m (k 1 ) m (k 2 ) ¥ k 1 m (m+n c b ) f n (n)dn f m (m)dm + ¥ m (k 1 ) ¥ k 1 m (m+n c b ) f n (n)dn f m (m)dm = ¥ m (k 2 ) " k 1 m k 2 m (m+n c b ) f n (n)dn # f m (m)dm + m (k 1 ) m (k 2 ) ¥ k 1 m (m+n c b ) f n (n)dn f m (m)dm +U b (k 1 ) Therefore, U b (k 2 )U b (k 1 ) = ¥ m (k 2 ) " k 1 m k 2 m (m+n c b ) f n (n)dn # f m (m)dm + m (k 1 ) m (k 2 ) ¥ k 1 m (m+n c b ) f n (n)dn f m (m)dm we can show both of the two terms on the right take negative values, the reasoning proceeds as following: First, since k 2 < k 1 < c b , m+n c b k 1 c b < 0 82 for anyn2[k 2 m; k 1 m]. It implies that k 1 m k 2 m (m+n c b ) f n (n)dn k 1 m k 2 m (k 1 c b ) f n (n)dn < 0 Therefore ¥ m (d 2 ) " k 1 m k 2 m (m+n c b ) f n (n)dn # f m (m)dm < 0 . Next, we consider m (k 1 ) m (k 2 ) ¥ k 1 m (m+n c b ) f n (n)dn f m (m)dm . By Lemma 3.3,m (k 2 )>m (k 1 ). So the above term can be rewritten as: m (k 2 ) m (k 1 ) ¥ k 1 m (m+n c b ) f n (n)dn f m (m)dm = m (k 2 ) m (k 1 ) [m+ E(njn k 1 m) c b ]Pr(n k 1 m) f m (m)dm < 0 where the last inequality holds because for anym2[m (k 1 ); m (k 2 )], m+ E(njn k 1 m) c b m (k 1 )+ E(njn k 1 m (d 1 )) c b = 0 . Therefore, U b (k 2 )U b (k 1 )< 0 , which means U b (k) increases with k when k< c b . 83 Combining the results above, we find that U b (k) is maximized at k = c b . And the number of consumers, N b = F B (U b (k)), also obtains its maximum at k= c b . Q.E.D. Lemma 3.5 The quality standard k which maximizes the platform’s profit must be k < c b . Proof: We have shown in Lemma 3.2 that the platform’s profit decreases with k, when k < c b . Therefore, the optimal standard k must fall into the interval(¥; c b ]. Next we prove step by step that k = c b is not the profit-maximizing point. (1). As illustrated in Lemma 3.4, U b (k) achieves its maximum at k= c b . And U b (k) is a differentiable function of k. Therefore we have ¶ U b (k) ¶k j k=c b = 0 (2). Next, we show that the number of sellers N s (k) decreases at the point k= c b . Recall that N s (k) = Pr(q k;mm (k)) = +¥ m (k) [1 F n (km)] f m (m)dm wheren =q+e. The first-order difference of N s (k) with respect to k equals to ¶ N s (k) ¶k =[1 F n (km (k))] f m (m (k)) ¶m (k) ¶k + +¥ m (k) [ f n (km)] f m (m)dm 84 . When k= c b , m (k)=¥ and 1 F n (km (k))= 0 . Therefore, ¶ N s (k) ¶k j k=c b = +¥ m (k) f n (km) f m (m)dm < 0 (3). If we take the first-order difference of the platform’s profit with respect to k, we obtain ¶ p M (k) ¶k j k=c b = b s f B (U b (k))(¶ U b (k) ¶k j k=c b )N s (k)+[b s F B (U b (k))t s ](¶ N s (k) ¶k j k=c b ) = 0+[b s F B (U b (k))t s ](¶ N s (k) ¶k j k=c b )< 0 . It means at the point k= c b , the platform can earn a larger profit by lowering the quality standard k. This result, together with Lemma 3.2, leads to the conclusion that the quality standard which maximizes the platform’s profit must satisfy k < c b . Q.E.D. According to Lemma 3.4 and Lemma 3.5, the optimal quality standards which respec- tively maximized consumer’s welfare and platform’s profit do not coincide with each other. From the perspective of consumers, the ideal screening is that the platform approves the entry of the products whose quality equals or larger than the consumer’s reservation value. But the platform needs to consider not only the participation of consumers, but also that of sellers, because it is the sizes on the two sides that jointly determine the total transaction 85 volume and the profit of the platform. The platform finds more profitable to set the standard lower than c b in order to have more sellers on board. Up to this point, we have been discussing one type of screening, the implementation of which is specified in Section 3.2.2. It remains unknown that whether the there exists another way of screening which generates more profits for the platform. Lemma 3.6 answers this question and compares the profits from two types of screenings. Lemma 3.6 In the following two types of implementing quality screening, the platform makes more profits through (1) than through (2): (1) Announce a quality standard k, and inform consumers of whether the quality of the product exceeds this standard or not: 1(q k); (2) Observe q and tell consumers the exact value of q; Proof: The type(1) screening is the one we have discussed in this paper. The consumer’s and seller’s equilibrium decisions have been analyzed in previous sections. Now let’s study the type(2) screening. If the platform observes q and tells consumers, consumers only choose the products of quality satisfying q c b , no matter of the product’s observable qualitym. Anticipating the consumer’s decisions, all sellers apply for joining the platform. If the quality revealed by the platform is larger than 86 c b , the seller continues to enter the platform. Otherwise the seller withdraws the application and quits from the market. Equivalently, the seller’s decision can be summarized as 1(enter the platform)= 1(q c b ) . According to above analysis, we can find that the strategies of consumers and sellers under type(2) screening are exactly the same as when the platform uses type(1) screening but chooses a standard k = c b . From Lemma 3.5, we know that k = c b is not the profit optimal one, and the platform can earn more if k < c b . Therefore, the platform obtains a larger profit in the case of type(1) screening. Q.E.D. The two alternatives proposed in Lemma 3.6 illustrate two ways that the platform can use to reveal information to consumers. Type(1) is partial information revelation, while Type(2) means full information revelation. It is easy to see that consumers prefer full infor- mation revelation, because this guarantees that consumers always make correct decisions and avoid picking up products of bad quality or leaving good products aside. But Type(1) screening is not consistent with the interests of the platform, which ultimately aims to max- imize the size of interactions between consumers and sellers. For this purpose, the platform finds it better to hold part of information from consumers and direct them to choose some products whose ex-post quality is less than c b . 87 3.4 Conclusion This chapter studies the effect of quality screening on the choices of consumers and sellers and the optimal screening standards for the monopoly platform. The equilibrium analysis shows when consumers hold asymmetric information about the quality, the commonly- known adverse selection problem happens and causes a welfare loss which is proportional to the consumer’s reservation value. The introduction of quality screening offers a way for sellers to signal their quality and helps to alleviate the adverse selection. Depending on the intensiveness of the screening, consumers can choose buy either from all sellers or from part of sellers. Accordingly, the seller’s optimal participation can be formalized as a pooling equilibrium or a separating equilibrium. This paper shows that consumers and the platform prefer different levels of screening standards. For consumers, the optimal standard which maximizes the ex-ante utility is equal to the consumer’s reservation value. But as the market maker, the platform cares the participation on the two sides, and finds it more profitable to choose a standard below the reservation value in order for more sellers to participate in the market. The paper also compares the platform’s profits under two different ways of information revelation: the first is partial revelation, which means the platform only tells consumers whether or not the product can pass the screening, and the second is to fully reveal the quality information to consumers. 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American Economic Review, 100 (4):1642–1672, 2010. Yiyi Zhou. Failure to launch in two-sided markets: A study of the us video game market. SSRN Scholarly Paper ID 2163948, 2013. Ting Zhu and Vishal Singh. Spatial competition with endogenous location choices: An application to discount retailing. Quantitative Marketing and Economics, 7(1):1–35, 2009. 91 Appendix A: Appendix to Chapter 2 This appendix provides the proof of Proposition 2.1 and 2.2. Proposition 2.1. (Equilibrium) Proof: Lemma 2.1. A seller joins Platform S if and only if its quality (m; q) satisfies the following condition: ln 1t S 1t NS + (l 1) l ln d S d NS +E(qjm; m= S)E(qjm; m= NS)+ ln(1 F e (k S mq)) 0 Proof: Seller j’s profit on Platform S can be expressed as p j;S (m j ;q j ; k S ;t S )= price j d j;S (1t S ) Pr(e j k S m j q j ) and its profit on Platform NS equals to p j;NS (m j ;q j ; k NS ;t NS )= price j d j;NS (1t NS ) . Therefore, the seller enters Platform S if and only if the log-profit on Platform S is larger than that on Platform NS, i.e., 92 4lnp j = lnp j;S (m j ;q j ; k S ;t s ) lnp j;NS (m j ;q j ; k NS ;t ns ) = ln 1t S 1t NS + ln d j;S d j;NS + ln(1 F e (k S m j q j )) (.1) 0 . Recall the demand function of seller j on platform m is d j;m = d jj j2J(m) d m = exp[u j;m ] å all j 0 2J(m) exp[u j 0 ;m ] exp[lEU m ] 1+å m 0 2fS;NSg exp[lEU m 0] = exp[E(q j jm j ; m) price j ] exp[(l 1)EU m ] 1+å m 0 2fS;NSg exp[lEU m 0] . Besides, ln d S d NS =l(EU S EU NS ) . The difference of log market shares on Platform S and NS, therefore, can be express as: ln d j;S d j;NS = E(q j jm j ; m= S)E(q j jm j ; m= NS)+(l 1)(EU S EU NS ) = E(q j jm j ; m= S)E(q j jm j ; m= NS)+ (l 1) l ln d S d NS = E(q j jm j ; m= S)E(q j jm j ; m= NS)+ (l 1) l ln d S d NS (.2) where the last equality is derived from the fact that: E(q j jm j ; m= S)=m j +E(q j jm j ;m= S) and E(q j jm j ; m= NS)=m j +E(q j jm j ;m= NS) 93 Combine (.1) and (.2), a seller with quality(m;q) joins Platform S if and only if ln 1t S 1t NS + (l 1) l ln d S d NS +E(qjm; m= S)E(qjm; m= NS)+ ln(1 F e (k S mq)) 0 (.3) Q.E.D. Lemma 2.2. When the observable quality m2(¥; k S qe), the seller chooses Platform S if and only if the unobservable quality q is larger than the threshold q (m), whereq (m) is the minimum point such that ln 1t S 1t NS + (l 1) l ln d S d NS +E(qjqq (m))E(qjqq (m))+ ln(1 F e (k S mq (m))) 0 . Ifq (m)2[q; ¯ q], there is a positive measure of type-m sellers on Platform S. Ifq (m)> ¯ q, none of type-m sellers enter Platform S. If q (m)<q, all type-m sellers participate in Platform S. Proof: We only prove the first part of Lemma 2.2. The second part is straight forward. As shown in Lemma 2.1, a type-m seller enters Platform S if and only if the inequality specified in (.3) holds. When m+q+e < k S , ln(1 F e (k S mq)) is a non-decreasing with respect toq, so does the left-hand side of (.3). Moreover, since ln(1F e (k S mq)) is bounded within(¥; 0], there exists a minimum pointq (m;d S ;d NS ; t S ;t NS ;k S )2R such that ln 1t S 1t NS + (l 1) l ln d S d NS +E(qjm; m= S)E(qjm; m= NS)+ln(1F e (k S mq (m;d S ;d NS ; t S ;t NS ;k S ))) 0 if ln 1t S 1t NS + (l 1) l ln d S d NS + supfE(qjm; m= S)E(qjm; m= NS)g> 0 94 . In equilibrium, the consumer’s belief ofq should coincide with the seller’s decision and take the form as follows: E(qjm; m= S)=E(qjqq (m;d S ;d NS ; t S ;t NS ;k S )) and E(qjm; m= NS)=E(qjqq (m;d S ;d NS ; t S ;t NS ;k S )) whereq (m;d S ;d NS ; t S ;t NS ;k S ) is determined by ln 1t S 1t NS + (l 1) l ln d S d NS +E(qjqq (m))E(qjqq (m))+ ln(1 F e (k S mq (m)))= 0 . For the short of notation, we denote q (m;d S ;d NS ; t S ;t NS ;k S ) as q (m) in the analysis hereafter. Q.E.D. Lemma 2.3. If the observable qualitym2(k S qe;+¥), the consumer’s belief ofq equals to E(qjm;m= S)=E(qjm;m= NS)= 0 and the seller enters Platform S if ln 1t S 1t NS + (l 1) l ln d S d NS > 0 and otherwise it chooses Platform NS. Proof: Whenm2(k S qe;+¥), for anyq2[q; ¯ q] ande2[e; ¯ e], we have Pr(m+q+e k S )= 1 95 , which means the seller of type-m can always pass the quality screening set by Platform S, no matter of its unobservable qualityq. In this case, the consumer is not able to update the information ofq based on the seller’s choice of platform. Therefore, we have E(qjm;m= S)=E(qjm;m= NS)=E(q)= 0 , following which the seller’s comparative profit on Platform S can be written as 4lnp = ln 1t S 1t NS + (l 1) l ln d S d NS . When ln 1t S 1t NS + (l 1) l ln d S d NS > 0 , the seller enters Platform S, i.e.,q (m)=q. Otherwise, the seller enters Platform NS, i.e., q (m)=q. Q.E.D. Using Lemma 2.1-2.3, now we prove Proposition 2.1. According to the sequence of the game, sellers move first to choose the desired plat- form and then consumers take actions. Therefore, when a seller weighs the profits on the two platforms, it needs to form an expectation about the the consumers’ responces in the next period, which, by Lemma 2.1, include the sharesfd S ;d NS g and the beliefE(qjm;m). Following Lemma 2.2 and Lemma 2.3,E(qjm;m) is ultimately determined byfd S ;d NS g. So the seller’s prior can be summarized as d e S = E(d S ) 96 and d e NS =E(d NS ) . In anticipation offd S ;d NS g, seller j participates in Platform S if its private signal q j satisfies: q j q (m j ) = q (m j ;d e S ;d e NS ) . And its conjecture about other sellers’ choices is E[1( j 0 2J(S);8 j 0 6= j)] = E[1(q j 0q (m j 0))] = E[1(q j 0q (m j 0;d S ;d NS ))] Now let’s analyze the consumer’s decision. Consumers participate in the platform which offers larger utility. And according to(2:5) and(2:6), the expected number of con- sumers that join platform m equals to E(d m ) =E 0 @ exp h l ln å j 0 2J(m) exp u j 0 ;m i 1+å m 0 2fS;NSg exp h l ln å j 0 2J(m 0 ) exp u j 0 ;m 0 i 1 A = E 0 B B B B @ exp " l ln N å j 0 =1 1( j 0 2J(S))exp u j 0 ;m !# 1+å m 0 2fS;NSg exp " l ln N å j 0 =1 1( j 0 2J(m))exp u j 0 ;m !# 1 C C C C A = G m (q (m j 0;d e S ;d e NS );fm j 0; price j 0g; j 0 = 1;:::N) 97 , which can be rewritten as a function offq (m j 0;d e S ;d e NS )g N j=1 . In equilibrium, seller j’s conjecture offd S ;d NS g should be consistent with the choices of consumers, that is, 2 6 6 4 d e S d e NS 3 7 7 5 = 2 6 6 4 G s (q (m j 0;d e S ;d e NS );fm j 0; price j 0g; j 0 = 1;:::N) G NS (q (m j 0;d e S ;d e NS );fm j 0; price j 0g; j 0 = 1;:::N) 3 7 7 5 G((q (m j 0;d e S ;d e NS );fm j 0; price j 0g; j 0 = 1;:::N)) . Since d e S ; d e NS 2 [0;1), by Brouwer Fixed Point Theorem, there must exist a pair of d e S ;d e NS satisfying above equation. Q.E.D. Proposition 2.2 (Comparative Statics) Proof: As illustrated in Proposition 2.1, when m2(¥; k S qe) ande Exp(l) , q (m) is determined by 0 = ln 1t S 1t NS + (l 1) l ln d S d NS +E(qjqq (m))E(qq (m))+ ln(1 F e (k S mq (m))) = ln 1t S 1t NS + (l 1) l ln d S d NS +E(qjqq (m))E(qq (m))+ l(m+q (m) k S ) By taking partial derivative with respect tom andq, we get ¶q (m) ¶m = l ¶E(qjqx) ¶x j x=q (m) ¶E(qjqx) ¶x j x=q (m) + l . Sinceq follows log-concave distribution, we know 0 ¶E(qjq x) ¶x 1 98 and 0 ¶E(qjq x) ¶x 1 Therefore, l 1 ¶E(qjq x) ¶x j x=q (m) ¶E(qjq x) ¶x j x=q (m) + l l+ 1 . Because l > 1, we can further have ¶q (m) ¶m < 0 Whenm2(k S q;+¥), as shown by Lemma 2.3, the threshold is given by q * (m)= 8 > > > > < > > > > : q if ln 1t S 1t NS + (l1) l ln d S d NS 0 ¯ q if ln 1t S 1t NS + (l1) l ln d S d NS < 0 Q.E.D. 99 Appendix B: Appendix to Chapter 3 This appendix provides the proof of Proposition 3.2. To facilitate the proof, we first show the following statement is true. Lemma 3.A. ˜ b(m;k) is an increasing function ofm. And lim m!+¥ ˜ b(m;k) = +¥ lim m!¥ ˜ b(m;k) = k c b Proof: We can write the consumer’s expected utility from the product as ˜ b(m;k) = E(qjm;q k) c b = E(m+q+ejq+e km) c b = m+ E(q+ejq+e km) c b 100 . According to Assumption 3.1, q and e are random variables with log-concave distribu- tions, it is easy to check q+e is also a random variable with a log-concave distribution. By An (1998), E(q+ejq+e km) satisfies: ¶ E(q+ejq+e km) ¶(km) 2(0;1) . Thus ¶ ˜ b(m;k) ¶m = 1+ ¶E(q+ejq+e km) ¶(km) (1)> 0 which means ˜ b(m;k) increases withm. Now let’s analyze the limit value of ˜ b(m;k). First whenm!+¥ lim m!+¥ ˜ b(m;k) = lim m!+¥ m+ E(q+ejq+e km) c b = lim m!+¥ m+ 0 c b = +¥ 101 and whenm!¥ lim m!+¥ ˜ b(m;k) = lim m!¥ m+ E(q+ejq+ekm) c b = lim m!¥ m+( ¥ km (q+e) f q+e 1 F q+e d(q+e) c b = k c b . Therefore lim m!+¥ ˜ b(m;k)=+¥ and lim m!+¥ ˜ b(m;k)= k c b Q.E.D. Proposition 3.2. Proof: Case1: k c b Seller’s problem We first solve the seller’s problem, taking consumers’ decision and the platform’s prices as given. Given each consumer purchases from all sellers on the platform, type-m seller’s expected profit from joining the platform is: p s (m;k) = Pr(q> k)[(b s p)N b (k)t s ] 102 . Because the seller is charged with a per-transaction fee p = b s t s N b (k) , the seller’s profit equals to p s (m;k) = 0 . All sellers have an incentive to enter the platform. Their applications are accepted when q k. So the number of sellers on the platform is N b (k) = Pr(q k) . Consumer’s problem: Given sellers’ entry decisions, the consumer’s expected utility of buying from type-m seller is ˜ b(m;k) = E(qjm;q k) c b = m+ E(q+ejq+e km) c b 103 . According to Lemma 3.A, ˜ b(m;k) is lower bounded by k c b , which is non-negative when k c b . The consumer, therefore, purchases from all sellers on the platform. The consumer’s total benefit from joining the platform is: U b (k)= E(q c b ;q k) . The number of consumers on the platform is N s (k)= F B (U b (k)) Platform’s problem The platform maximizes its profit by choosing the optimal per-transaction fee, p, and standard, k such that max p;k p(p;k) = p N b (k) N s (k) s.t. p s (m;k) 0 where p s (m;k)= Pr(q k)[(b s p)N b (k)t s ] . It’s easy to verify that the optimal per-transaction is p = b s t s N b (k) 104 . Then the platform’s problem can be rewritten as max kc b p(k)=[b s F B (U b (k))t s ]Pr(q k) , from which the optimal standard k is determined. Case2: k< c b Seller’s problem Given consumers’ purchasing decision, sellers withm <m (k) do not apply for joining the platform, because they know that even if their products can pass the screening and enter the platform, they cannot make any sales. Sellers with m m (k) can make sales once they enter the platform. Their expected profit is p s (m;k) = Pr(q k)[(b s p)N b (k)t s ] . Similar to Case 1, for incentive compatibility, the seller’s expected profit cannot be nega- tive, i.e., p s (m;k) 0() p b s t s N b (k) . This condition holds as the platform sets the price p = b s t s N b (k) 105 . The number of sellers that pass screening and enter the platform is: N s (k) = Pr(q k;mm (k)) = Pr(m+q+e k;mm (k)) = ¥ m (k) [1 F q+e (km)] f m dm Consumer’s problem The consumer’s expected utility of buying from the type-m seller is ˜ b(m;k) = E(qjm;q k) c b = m+ E(q+ejq+e km) c b . By Lemma 3.A, ˜ b(m;k) increases with m and is bounded in(k c b ;+¥) . When k< c b , the lower bound of ˜ b(m;k) is negative. There exists a unique pointm (k)<¥ such that for allmm (d), the following inequality holds: m+ E(q+ejq+e km) c b 0 . Therefore, the consumer purchases from the sellers with observable quality m >m (d) . The consumer’s total benefit from joining the platform can be expressed as U b (k)= E(q c b ;q k;mm (k)) 106 . The number of consumers on the platform is N s (k) = F B (U b (k)) Platform’s problem Similar to Case 1, the platform determines the per-transaction fee to be p = b s t s N b (k) . The quality standard is given by max k<c b p(k) = [b s F B (U b (k))t s ]Pr(q k;m >m (k)) Q.E.D. 107

Abstract (if available)

Abstract In two-sided markets, consumers care not only about the number of sellers with which they can interact, but also about the quality of products or services these sellers provide. Previous work on two-sided markets has mainly focused on the quantity externality

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Creator Wang, Jin (author)

Core Title Essays on quality screening in two-sided markets

School College of Letters, Arts and Sciences

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Publication Date 07/28/2015

Defense Date 05/11/2015

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Advisor Tan, Guofu (committee chair), Dukes, Anthony (committee member), Ridder, Geert (committee member)

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