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Robust Market Design: Information and Computation ROBUST MARKET DESIGN: INFORMATION AND COMPUTATION A DISSERTATION SUBMITTED TO THE DEPARTMENT OF COMPUTER SCIENCE AND THE COMMITTEE ON GRADUATE STUDIES OF STANFORD UNIVERSITY IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY Inbal Talgam-Cohen December 2015 Abstract A fundamental problem in economics is how to allocate precious and scarce resources, such as radio spectrum or the attention of online consumers, to the benefit of society. The vibrant research area of market design, recognized by the 2012 Nobel Prize in economics, aims to develop an engineering science of allocation mechanisms based on sound theoretical foundations. Two central assumptions are at the heart of much of the classic theory on resource allocation: the common knowledge and substitutability assumptions. Relaxing these is a prerequisite for many real-life applications, but involves significant informational and computational challenges. The starting point of this dissertation is that the computational paradigm offers an ideal toolbox for overcoming these challenges in order to achieve a robust and applicable theory of market design. We use tools and techniques from combinatorial optimization, randomized algo- rithms and computational complexity to make contributions on both the informa- tional and computational fronts: 1. We design simple mechanisms for maximizing seller revenue that do not rely on common knowledge of buyers' willingness to pay. First we show that across many different markets { including notoriously challenging ones in which the goods are heterogeneous { the optimal revenue benchmark can be surpassed or approximated by adding buyers or limiting supplies, and then applying the standard Vickrey (second-price) mechanism. We also show how, by removing the common knowledge assumption, the classic theory of revenue maximiza- tion expands to encompass the realistic but complex case in which buyers are interdependent in their willingness to pay. iv 2. We prove positive and negative results for maximizing social welfare without substitutability, i.e., without the convexity property known to drive economic efficiency. On the positive side, we design natural greedy mechanisms for two- sided markets with strong incentive properties, whose welfare performance de- pends on the market's \distance" from substitutability. On the negative side, we show how computational challenges related to complementarity lead to the economic failure of competitive markets, in the sense that there do not exist simple prices that guide such a market to an efficient allocation. These results carry implications for the practice of market design, both for revenue- maximizing sellers such as Internet companies running online auctions, and for welfare- maximizing policy makers such as governments running spectrum auctions. v In loving memory of Daphna Talgam Acknowledgements Although I spent many hours of solitary work towards this dissertation, the most meaningful and memorable parts were the interaction and collaboration with my advisors, mentors, colleagues and friends. First and foremost I would like to thank my advisor Tim Roughgarden. Working under his guidance has been an enormous privilege, and he will always be an inspi- ration for me in the depth and breadth of his knowledge and insight, his passion for teaching and mentoring, his integrity, curiosity and daring intellectual, his leadership and generosity to his students. I also wish to thank my mentor Paul Milgrom. Taking his course my second year at Stanford was a turning point in my life, and like so many others I have been profoundly influenced by his genius (as is apparent throughout this dissertation). I am deeply grateful for his support and for all that I have learned through our conversations. I thank Ramesh Johari for kindly serving on my reading committee and for his excellent guidance in writing this dissertation, Robert Wilson for doing me the honor of chairing my dissertation committee, and Ashish Goel for kindly serving on the committee. Thanks to my wonderful co-authors Qiqi Yan and Paul Duetting, without whom parts of this dissertation would not have come to existence. I was fortunate to learn from Qiqi's originality and modesty, and Paul's clarity of thought and productivity. I thank the Hsieh family for honoring me with the title of Hsieh Fellow and for generously funding my research. vii I wish to acknowledge those without whom I would not have begun my PhD stud- ies: Special thanks to Uriel Feige, my MSc advisor at the Weizmann Institute, whose profound wisdom and concise, on-spot advice have guided me throughout my PhD studies. I thank Justice Esther Hayut for allowing me the honor and privilege of in- terning with her; witnessing firsthand how her deep thinking and economic reasoning drove fairness and justice inspired me to pursue this PhD. I owe a great deal to many researchers at Stanford who were always available to provide invaluable advice and guidance: Itai Ashlagi, Yonatan Gur, Fuhito Kojima, Uri Nadav, Serge Plotkin, Al Roth, Amin Saberi, Yoav Shoham, Gregory Valiant, Ryan Williams and Virginia Vassilevska Williams. Special thanks to Vasilis Gkatzelis for his generosity and encouragement. Heartfelt thanks to the mentors, collaborators and co-authors with whom I was fortunate to connect through my internships and research projects: Noga Alon, Moshe Babaioff, Shahar Dobzinski, Michal Feldman, Prabhakar Krishnamurthy, Mohammad Mahdian, Yishai Mansour, Mukund Sundararajan, Moshe Tennenholtz, Sergei Vas- silvitskii, L´aszl´oV´eghand Omri Weinstein. Thanks to those who made Stanford such a wonderful place for me: Tim's group members (Peerapong, Shaddin, Rishi, Zhiyi, Anthony, Kostas, Jamie, Okke and Joshua), the members of the market design coffee, and admins Lynda Harris and Ruth Harris. I am grateful to the folks at ACM for entrusting me with co-leading XRDS maga- zine, an experience which introduced me to many brilliant peers, enriched my knowl- edge of the computer science community and made me a better community member. Thanks to my dear friends in the Bay Area, for helping me get through the difficult times and celebrate the good ones: Ayelet, Elinor, Gili, Ifat, Neta and Shiri, as well as Ankita, Erika, Kahye, Kshipra, Irene and Leor, Keren and Orit, and finally Dana. I am grateful beyond words to my parents Yoav and Daphna, brothers Erez and Tomer and family members Ruti, Efrat, Avi and Dorit for their love and support. And to Noy, thank you for standing by me always and for sharing this incredible journey with me, which you and Dory have made so special. viii Contents Abstract iv vi Acknowledgements vii 1 Introduction 2 1.1 Overview ..................................................................... 2 1.2 Model......................................................................... 6 1.2.1 Basic Model .......................................................... 6 1.2.2 Revenue: Bayesian Model and Interdependence ................... 9 1.2.3 Welfare: Substitutes ................................................. 11 1.2.4 Solution Concepts ................................................... 12 1.3 Motivating Examples and Related Literature ............................. 15 1.3.1 Motivating Examples ................................................ 15 1.3.2 Market Design State-of-the-Art .................................... 17 1.4 Research Goals ............................................................... 20 1.4.1 Goal 1: Revenue without Common Knowledge.................... 20 1.4.2 Goal 2: Welfare without Substitution .............................. 24 1.4.3 Meta-Goal: Simplicity............................................... 29 1.5 Contributions ................................................................ 31 1.5.1 Informational Contributions in Revenue Maximization ........... 31 1.5.2 Computational Contributions in Welfare Maximization .......... 36 1.6 Bibliographic Notes .......................................................... 42 ix 2 Preliminaries 43 2.1 Auction Environments....................................................... 43 2.1.1 Single-Parameter Bayesian Environments ......................... 43 2.1.2 Multi-Parameter Matching Environments ......................... 45 2.2 Optimal Mechanism Design ................................................. 46 2.2.1 Mechanisms .......................................................... 46 2.2.2 Maximizing Welfare and the Vickrey Auction ..................... 47 2.2.3 Maximizing Revenue and Myerson's Mechanism .................. 48 2.2.4 Regularity ............................................................ 49 2.3 Prior-Independent Robustness .............................................. 49 2.3.1 Definition............................................................. 49 2.3.2 Rationales ............................................................ 51 2.3.3 Robustness in the Literature........................................ 52 I Informational Challenges in Revenue Maximization 54 3 Robust Revenue Maximization in Matching Markets 55 3.1 Chapter Introduction ........................................................ 55 3.1.1 Overview ............................................................. 55 3.1.2 The Problem ......................................................... 56 3.1.3 Motivating Example: Multi-Unit Markets ......................... 58 3.1.4 Our Contribution .................................................... 62 3.1.5 Related Work ........................................................ 65 3.1.6
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