Network Markets and Coordination Games A Dissertation Presented to the Faculty of the Graduate School of Yale University in Candidacy for the Degree of Doctor of Philosophy by Rosa Argenziano Dissertation Directors: Professor Dirk Bergemann and Professor Stephen Morris May 2005 Contents Acknowledgments v Introduction 1 1Differentiated Networks: Equilibrium and Efficiency 5 1.1Introduction.................................... 5 1.2TheModel.................................... 10 1.3 EfficientAllocation................................ 15 1.4TheEquilibriumAllocation........................... 23 1.4.1 ConsumerCoordination......................... 24 1.4.2 UnsponsoredNetworks.......................... 28 1.4.3 SponsoredNetworks........................... 30 1.5Conclusions.................................... 33 2 Network Markets and Consumer Coordination1 36 2.1Introduction.................................... 36 2.2RelatedLiterature................................ 42 2.3TheModel.................................... 44 2.4 Coalitional Rationalizability and Coalition Perfect Equilibrium . 46 2.5MonopolistwithOneNetwork.......................... 51 2.6MonopolistWhoCanOperateMultipleNetworks............... 53 2.6.1 TwoTypesofConsumersonEachSide................ 54 2.6.2 General Specification........................... 61 2.7Duopoly...................................... 62 2.7.1 HomogeneousConsumers........................ 63 2.7.2 TheGeneralCase............................ 66 2.8Discussion..................................... 70 2.8.1 PositiveMarginalCost.......................... 70 2.8.2 Multi-Homing............................... 71 2.8.3 Conflict of Interest among Consumers on the Same Side . 71 2.8.4 MorethanTwoFirms.......................... 72 2.9ConclusionsandPossibleExtensions...................... 73 1 Attila Ambrus and Rosa Argenziano i CONTENTS ii 3 History as a Coordination Device2 74 3.1Introduction.................................... 74 3.2RelatedLiterature................................ 77 3.3TheStageGame................................. 78 3.4WhereDoExpectationsComefrom?...................... 83 3.5TheDynamicProcess.............................. 87 Appendices 91 A 92 B 109 C 131 Bibliography 135 2 Rosa Argenziano and Itzhak Gilboa List of Figures 1.1 Aggregate surplus derived from the vertical quality of the goods for the case θ =2. ....................................... 19 1.2 Aggregate surplus derived from idiosyncratic taste for the case θ =2. .... 21 1.3 Aggregate surplus derived from the network effect for the case θ =2. .... 22 2.1 Optimal Price Structure for a Monopolist with Two Networks . 59 3.1 Threshold p∗(x) .................................. 82 iii c 2005 by Rosa Argenziano ° All rights reserved. Acknowledgments I am deeply indebted to Dirk Bergemann and Stephen Morris for their constant support, their detailed feedback and their infinite patience. The guidance, help and encouragement I received from them in the last five years were more than any doctoral student could have asked for. When I work on my research, I tend to commit at least two mistakes. First, I often develop confused ideas and equations and get lost into them. Stephen’s ability to see clearly through my confusion and find the potentially interesting element hidden in there has been invaluable. Second, I tend to underestimate what I can achieve. Dirk’s wise but firm unwillingness to believe me every time I announced that I had done "my best" has constituted a constant challenge for which I will never thank him enough. I am also grateful to Dino Gerardi for his encouragement, his irony, and all his precious, constructive suggestions and to Ben Polak for his support and his generous attention to every detail of my work. A special thanks goes to Don Brown for his patience, his enthusiasm and the long afternoons he spent listening to my attempts to prove some lemma. And for the chocolate. Chapter 2 of this dissertation is coauthored with Attila Ambrus, to whom I am deeply grateful for the incredible amount of work he invested in our project. His deep understanding of game theory and his dedication to his work have been a real source of inspiration for me. Chapter 3 of this dissertation is coauthored with Itzhak Gilboa, a true Renaissance man from whom I learnt, among innumerable other things, that a sincere intellectual curiosity is a necessary condition to enjoy life as a researcher. I also thank Bernard Caillaud, Giancarlo Corsetti, Jacques Cremer, Gergely Csorba, Ulrich Doraszelvski, Erica Field, Ezra Friedman, Drew Fudenberg, Bernardo Guimaraes, Barry O’Neill, Ady Pauzner, Alessandro Pavan, Ben Polak, Dmitry Shapiro, Hyun Song Shin, Gábor Virág and seminar participants at Yale University, Harvard University, Olin School of Business, at the Conference on Two-Sided Markets and at the Conference on The Economics of Software and the Internet organized by IDEI Toulouse, at the 31st TPRC, at the 2004 Winter Meeting of the Ec PAC Project and at the WISE workshop in Salerno for helpful comments and discussions. This dissertation would have never been written if I had not taken Riccardo Martina’s undergraduate microeconomics class. He has the gift to share with his students much more than his knowledge of economics: he shares with them his passion for it. In the last eleven years he has been a great teacher and a true friend and I will always be grateful for his constant encouragement. I consider myself extremely lucky for the chance I had to spend the last five years in the Economics Department at Yale University. Here I found not only dedicated teachers and inspiring advisors, but also a warm and friendly work environment, and colleagues from whom I have learnt something new every day. Finally, I want to thank Pam O’Donnell, for being a mother away from home. I gratefully acknowledge financial support from the Cowles Foundation and from Yale University in the form of a Robert M. Leylan Dissertation Fellowship. To my parents, Tina and Salvatore, for teaching me to follow my dreams To Sergio, for sharing those dreams Introduction Several oligopolistic industries that play a crucial role in modern economies are "network industries": industries where the benefit that an individual consumer derives from consum- ing a good increases with the number of other people consuming the same good. Network markets can be one-sided or two-sided. Examples of the first class of markets are soft- ware markets: the utility an individual derives from a given software is increasing in the total number of users because the more people own the software, the more people they can interact with, exchanging files and know-how. The second class of markets includes auction websites, credit card networks, directory services and all those markets where two groups of individuals or firms need a common platform to interact and one or more firms own platforms and sell access to them. In this case, the utility derived from accessing a platform is increasing in the number of potential counterparts who join the same platform. Also, network products can be divided into pure network goods, such as telecommunication networks, and non-pure network goods. The first class of products includes all those goods for which the network externality is the only source of utility a consumer derives from the product, while the second class includes al those products that also provide an intrinsic utility. 1 2 A classic methodological issue related to network markets is that modeling the demand function is particularly challenging because the problem faced by consumers choosing which network to join, for given prices, constitutes a coordination game and typically coordination games have multiple equilibria. My dissertation explores three different approaches to this problem. In chapter 1, I analyze one-sided markets for non-pure network goods where consumers can choose between two alternative products that are both vertically and horizontally dif- ferentiated. Modeling consumer choice as a global game with private values, I show that either a large amount of horizontal differentiation or a high positive correlation of con- sumers’ private values of the goods are necessary and sufficient for the demand function to be well-defined. Using this result, I then address the issue of efficiency on these mar- kets. I derive the equilibrium allocation of consumers to the networks for both the case of sponsored and unsponsored networks as well as the allocation that would maximize social welfare. The three allocations share two important features: in all of them both networks are active, due to the presence of sufficiently strong horizontal differentiation, and the high quality network attracts more than one half of the consumers. Nonetheless, two inefficien- cies arise. First, since consumers fail to internalize network externalities, the equilibrium allocation with unsponsored networks is too balanced. Second, if access to the networks is priced by strategic firms, then the firm with a higher expected quality charges a price higher than the competitor’s and this further reduces the asymmetry between market shares and therefore social welfare. In chapter 2, which is coauthored with Attila Ambrus, we analyze two-sided markets for 3 pure network goods. We address the issue of multiple equilibria of the coordination game played by consumers, assuming that the latter can coordinate their decisions to their advan- tage, if their interests coincide and if coordination can be achieved without communication. Using this methodology, we show that multiple