ABSTRACT ESSAYS on AUCTION DESIGN Haomin Yan Doctor of Philosophy, 2018 Dissertation Directed By: Professor Lawrence M. Ausubel
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ABSTRACT Title of dissertation: ESSAYS ON AUCTION DESIGN Haomin Yan Doctor of Philosophy, 2018 Dissertation directed by: Professor Lawrence M. Ausubel Department of Economics This dissertation studies the design of auction markets where bidders are un- certain of their own values at the time of bidding. A bidder's value may depend on other bidders' private information, on total quantity of items allocated in the auction, or on the auctioneer's private information. Chapter 1 provides a brief introduction to auction theory and summarizes the main contribution of each following chapter. Chapter 2 of this dissertation ex- tends the theoretical study of position auctions to an interdependent values model in which each bidder's value depends on its opponents' information as well as its own information. I characterize the equilibria of three standard position auctions under this information structure, including the Generalized Second Price (GSP) auctions, Vickrey-Clarke-Groves (VCG) auctions, and the Generalized English Auc- tions (GEA). I first show that both GSP and VCG auctions are neither efficient nor optimal under interdependent values. Then I propose a modification of these two auctions by allowing bidders to condition their bids on positions to implement ef- ficiency. I show that the modified auctions proposed in this chapter are not only efficient, but also maximize the search engine's revenue. While the uncertainty of each bidder about its own value comes from the presence of common component in bidders ex-post values in an interdependent values model, bidders can be uncertain about their values when their values depend on the entire allocation of the auction and when their values depend on the auctioneer's private information. Chapter 3 of this dissertation studies the design of efficient auctions and optimal auctions in a license auction market where bidders care about the total quantity of items allocated in the auction. I show that the standard uniform-price auction and the ascending clock auction are inefficient when the total supply needs to be endogenously determined within the auction. Then I construct a multi-dimensional uniform-price auction and a Walrasian clock auction that can implement efficiency in a dominant strategy equilibrium under surplus-maximizing reserve prices and achieve optimal revenue under revenue-maximizing reserve prices. Chapter 4 of this dissertation analyzes an auctioneer's optimal information provision strategy in a procurement auction in which the auctioneer has private preference over bidders' non-price characteristics and bidders invest in cost-reducing investments before entering the auction. I show that providing more information about the auctioneer's valuation over bidders' non-price characteristics encourages those favored bidders to invest more and expand the distribution of values in the auction. Concealment is the optimal information provision policy when there are two suppliers. ESSAYS ON AUCTION DESIGN by Haomin Yan Dissertation submitted to the Faculty of the Graduate School of the University of Maryland, College Park in partial fulfillment of the requirements for the degree of Doctor of Philosophy 2018 Advisory Committee: Professor Lawrence M. Ausubel, Chair/Advisor Professor Daniel R. Vincent Professor Emel Filiz-Ozbay Professor Ginger Zhe Jin Professor Mohammad Hajiaghayi c Copyright by Haomin Yan 2018 Acknowledgments I owe my gratitude to all the people who made this dissertation possible. It is my great pleasure to thank them here. First, I would like to thank my primary advisor, Professor Lawrence Ausubel for his continuous support, guidance and encouragement over the past few years. It has been my honor to learn from and be guided by a leading scholar in auction theory. I am indebted to him for inspiring my interests in auction theory, giving many thoughtful comments on my work, and providing me a lot of encouragement and support during my years in graduate school. It would be impossible for me to have finished this dissertation without his support. I would also like to thank Professor Daniel Vincent for his guidance and many helpful comments on my thesis. I am indebted to him for many hours of discussion about formulating research ideas, constructing models, and fining details of analyses and proofs. His expertise in mechanism design, microeconomic theory, and indus- trial organization theory has inspired my interests in these fields and expanded my research ideas. I want to thank Professor Emel Filiz-Ozbay for her continuous support and helpful suggestions. My thesis has been greatly benefited from the many hours of discussion with her. Her guidance has deepened my understanding and broaden my interests in microeconomic theory. I want to thank Professor Ginger Zhe Jin and Professor Mohammad Hajiaghayi for agreeing to serve on my thesis committee and for sparing their invaluable time ii reviewing the manuscript. I also want to thank all the professors, discussants, and fellow graduate stu- dents who attended my presentations in the University of Maryland, 2017 Young Economist Symposium, 2017 Midwest Economic Theory Conference, 12th Annual Economic Graduate Student Conference, and US Naval Academy for their comments and questions, especially Professor Lawrence Ausubel, Professor Daniel Vincent, Professor Emel Filiz-Ozbay, Professor Ginger Zhe Jin, Professor Erkut Ozbay, Pro- fessor Andrew Sweeting, Professor Guido Kuersteiner, Professor Roger Betancourt, Professor Jessica Goldberg, Professor Judith Hellerstein, Professor Naomi Utgoff, Professor Karen Thierfelder, Professor Alex McQuoid, Ian Ball, Nicolas Inostroza, Tzu-Yao Lin, Gustavo Saraiva, and Xuezhen Tao. Their comments have helped me to improve my work. I want to thank my undergraduate advisors, Professor Mahnaz Mahdavi, Pro- fessor Elizabeth Savoca, and Professor Susan Stratton Sayre, for encouraging me to pursue doctoral degree in economics, guiding my undergraduate research, and recommending me for admission to the University of Maryland. I am also grateful for the friendship and support I have received from my friends, especially Diyue Guo, Shen Hui, Yidan Jin, Youpei Yan, Feng Zhang, and Shikun Zhang. I want to thank them for helping me and encouraging me during the most difficult times in my graduate school journey. I wish them a bright and successful future. I would also like to acknowledge help and support from the Director of Grad- uate Studies, Professor John Shea, and the staff members in the Economics De- iii partment of University of Maryland, especially Terry Davis, Vickie Fletcher, Brian Mcloughlin, Amanda Statland, and Mark Wilkerson. Finally, I owe my deepest thanks to my family - my mother, Jie Wu, and my father, Zhexin Yan, who have always encouraged me to pursue my dreams, helped me to achieve my goals, and supported me in every way over the years. I would not have been able to go this far without their encouragement and support. Words cannot express the gratitude I owe them. iv Table of Contents Acknowledgements ii List of Figures vii List of Abbreviations viii 1 Introduction1 1.1 Introduction................................1 1.2 Summary of Contributions........................4 2 Position Auctions with Interdependent Values8 2.1 Introduction................................8 2.2 Related Literature............................ 16 2.3 Model................................... 21 2.4 Inefficiency of One-dimensional Position Auctions........... 24 2.4.1 One-dimensional Position Auctions............... 25 2.4.2 Characterization of Equilibrium................. 27 2.4.3 Efficiency Analysis........................ 30 2.5 Efficiency of K-dimensional Position Auctions............. 34 2.5.1 K-dimensional Position Auctions................ 34 2.5.2 Characterization of Equilibria and Efficiency Analysis..... 37 2.5.2.1 Equilibrium of K-dimensional GSP Auction..... 38 2.5.2.2 Equilibrium of K-dimensional VCG Auction..... 40 2.5.2.3 Equilibrium of Generalized English Auction..... 44 2.6 Revenue of K-dimensional Position Auctions.............. 47 2.6.1 Revenue Ranking......................... 47 2.6.2 Revenue Comparison with the Optimal Position Auction... 49 2.6.2.1 Mechanism Design and Solution Concepts...... 50 2.6.2.2 Characterization of the Optimal Position Auction.. 52 2.6.2.3 Revenue Comparison.................. 54 2.7 Conclusions................................ 57 v 3 Auctions with Quantity Externalities and Endogenous Supply 61 3.1 Introduction................................ 61 3.2 Related Literature............................ 64 3.3 Model................................... 68 3.4 An Efficient Direct Mechanism...................... 72 3.5 Practical Implementation of Efficient Auctions............. 75 3.5.1 Uniform-Price Auction with Endogenous Supply........ 77 3.5.2 Ascending Clock Auction with Endogenous Supply...... 84 3.5.3 Multi-dimensional Uniform-price Auction............ 89 3.5.4 Walrasian Clock Auction..................... 92 3.6 An Optimal Direct Mechanism...................... 96 3.6.1 Mechanism Design and Solution Concepts........... 96 3.6.2 Characterization of the Optimal Auction Mechanism..... 97 3.7 Auction Design under Consideration of Consumer Surplus...... 103 3.8 Conclusions................................ 106 4 Information Provision in Procurement Auctions with Endogenous Invest- ments 108 4.1 Introduction................................ 108 4.2 Related Literature............................ 111 4.3 Model................................... 113 4.3.1 Environment........................... 113 4.3.2 Equilibrium