Dynamic Strategic Interactions: Analysis and Mechanism Design by Utku Ozan Candogan B.S., Electrical and Electronics Engineering, Bilkent University (2007) M.S., Electrical Engineering and Computer Science, Massachusetts Institute of Technology (2009) Submitted to the Department of Electrical Engineering and Computer Science in partial fulfillment of the requirements for the degree of ARCHN&S Doctor of Philosophy MASSACHUSETTS INSTY TE OF TECHNOLOGY at the JUL 0 8 2013 MASSACHUSETTS INSTITUTE OF TECHNOLOGY June 2013 LIBRARIES @ Massachusetts Institute of Technology 2013. All rights reserved. Author.......................................................... Department of Electrical Engineering and Computer Science May 22, 2013 C ertified by ........................... ky Asuman zdaglar ,1 Professor Thesis Supervisor C ertified by ................................. --............ ........ Pablo A. Parrilo Professor V, Thesis Supervisor Accepted by ..... 4lie A. Kolodziejski Professor Chair, Department Committee on Graduate Students 2 Dynamic Strategic Interactions: Analysis and Mechanism Design by Utku Ozan Candogan Submitted to the Department of Electrical Engineering and Computer Science on May 22, 2013, in partial fulfillment of the requirements for the degree of Doctor of Philosophy Abstract Modern systems, such as engineering systems with autonomous entities, markets, and finan- cial networks, consist of self-interested agents with potentially conflicting objectives. These agents interact in a dynamic manner, modifying their strategies over time to improve their payoffs. The presence of self-interested agents in such systems, necessitates the analysis of the impact of multi-agent decision making on the overall system, and the design of new systems with improved performance guarantees. Motivated by this observation, in the first part of this thesis we focus on fundamental structural properties of games, and exploit them to provide a new framework for analyzing the limiting behavior of strategy update rules in various game-theoretic settings. In the second part, we investigate the design problem of an auctioneer who uses iterative multi-- item auctions for efficient allocation of resources. More specifically, in the first part of the thesis we focus on potential games, a special class of games with desirable equilibrium and dynamic properties, and analyze their preference structure. Exploiting this structure we obtain a decomposition of arbitrary games into three components, which we refer to as the potential, harmonic, and nonstrategic components. Intuitively, the potential component of a game captures interactions that can equivalently be represented as a common interest game, while the harmonic part represents conflicts between the interests of the players. We make this intuition precise by studying the properties of these two components, and establish that indeed they have quite distinct and remarkable characteristics. The decomposition also allows us to approximate a given game with a potential game. We show that the set of approximate equilibria of an arbitrary game can be characterized through the equilibria of a potential game that approximates it. The decomposition provides a valuable tool for the analysis of dynamics in games. Earlier literature established that many natural strategy update rules converge to a Nash equilibrium in potential games. We show that games that are close to a potential game exhibit similar properties. In particular, we focus on three commonly studied discrete-time update rules (better/best response, logit response, and discrete-time fictitious play dynam- ics), and establish that in near-potential games, the limiting behavior of these update rules can be characterized by an approximate equilibrium set, size of which is proportional to the distance of the original game from a potential game. Since a close potential game to a given game can be systematically found via decomposition, our results suggest a systematic framework for studying the limiting behavior of adaptive dynamics in arbitrary finite strate- gic form games: the limiting behavior of dynamics in a given game can be characterized by first approximating this game with a potential game, and then analyzing the limiting behavior of dynamics in the potential game. 3 In the second part of the thesis, we change our focus to implementing efficient out- comes in multi-agent settings by using simple mechanisms. In particular, we develop novel efficient iterative auction formats for multi-item environments, where items exhibit value complementarities/substitutabilities. We obtain our results by focusing on a special class of value functions, which we refer to as graphical valuations. These valuations are not fully general, but importantly they capture value complementarity/substitutability in important practical settings, while allowing for a compact representation of the value functions. We start our analysis by first analyzing how the special structure of graphical valuations can be exploited to design simple iterative auction formats. We show that in settings where the underlying value graph is a tree (and satisfies an additional technical condition), a Walrasian equilibrium always exists (even in the presence of value complementarities). Using this result we provide a linear programming formulation of the efficient allocation problem for this class of valuations. Additionally, we demonstrate that a Walrasian equilibrium may not exist, when the underlying value graph is more general. However, we also establish that in this case a more general pricing equilibrium always exists, and provide a stronger linear programming formulation that can be used to identify the efficient allocation for general graphical valuations. We then consider solutions of these linear programming formulations using iterative algorithms. Complementing these iterative algorithms with appropriate payment rules, we obtain iterative auction formats that implement the efficient outcome at an (ex-post perfect) equilibrium. The auction formats we obtain rely on simple pricing rules that, in the most general case, require offering a bidder-specific price for each item, and bidder-specific discounts/markups for pairs of items. Our results in this part of the thesis suggest that when value functions of bidders exhibit some special structure, it is possible to systematically exploit this structure in order to develop simple efficient iterative auction formats. Thesis Supervisor: Asuman Ozdaglar Title: Professor Thesis Supervisor: Pablo A. Parrilo Title: Professor 4 To my families: past, present, and future. 5 6 Acknowledgments Being a doctoral student at one of the most intellectually stimulating schools in the world has been a privilege. However, for me perhaps the most exciting and gratifying component of my MIT experience has been the opportunity to work with my advisors Asu Ozdaglar and Pablo Parrilo. Their guidance, combined with their endless support and enthusiasm made this thesis possible. Additionally, the nurturing and friendly research environment they created for their students at MIT, which is filled with innate curiosity and interesting ideas, has been essential for my development as a scholar and a researcher. I, with no doubt, have been very fortunate to complete my doctoral studies under their supervision. Both Asu and Pablo are outstanding examples for me, and I will try my best to carry their inspiration and guidance throughout my life. I am also grateful to Prof. Georgia Perakis, and Prof. Daron Acemoglu for serving on my thesis committee. Their insights and perspective inspired me to refine and improve the ideas that are central to thesis, and discover new applications for my results. Consequently, this thesis has benefited enormously from their comments and feedback. I have also been very lucky to have their guidance and support in the job market. I would like to thank them for their dedication and help. I am indebted to faculty members at LIDS, ORC, and CSAIL, especially to John Tsitsiklis, Devavrat Shah, Munther Dahleh, Itai Ashla Vivek Farias, and Constantinos Daskalakis for creating a diverse and rich learning environment at MIT. Their lectures, ideas, and talks have been both inspiring and stimulating. I have learned vastly from my other coauthors as well: Kostas Bimpikis, Ilan Lo- bel, Hamid Nazerzadeh, Jennifer Chayes, Christian Borgs, Ishai Menache, Constantinos Daskalakis, and Christos Papadimitriou. I have been extremely fortunate to work with some of these brightest minds from different communities. I look forward to interacting more with them, and having many other fruitful collaborations. I also want to thank Kostas, Ilan, and Hamid, for being great friends who are always willing to listen. I am deeply grateful to (past and present) members of the Microsoft Research lab in New England, in particular, Jennifer Chayes, Christian Borgs, Ishai Menache, Adam Kalai, Sham Kakade, Brendan Lucier, and Yash Kanoria. In addition to the excellent talks and workshops I attended at Microsoft Research, my interaction with the members of the lab during my internships enriched my experience as a scholar, and exposed me to different ideas and perspectives. Also a special thanks goes to Jennifer for her support and help during my job search. Various friends from ORC and LIDS made MIT a second home for me. I especially would like to thank Alireza Tahbaz-Salehi, Ercan Yildiz, Mohamed Mostagir, Azarakhsh Malekian, Christina Lee, Diego Feijer, Ali ParandehGheibi,