Bounded Rationality and Mechanism Design Dissertation Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By Luyao Zhang, M.A. Graduate Program in Economics The Ohio State University 2018 Dissertation Committee James Peck, Advisor Dan Levin, Co-Advisor Paul J. Healy 1 Copyrighted by Luyao Zhang 2018 2 Abstract Mechanism Design Theory, introduced by 2007 Nobel laureates Hurwicz, Maskin, and Myerson, has guided economic institutions worldwide to achieve desirable goals in allocating scarce resources. However, most of the literature on Mechanism Design Theory that guides its application, in reality, assumes that people are fully rational; this omission of people’s bounded rationality raises doubt over the reliability of the theory’s empirical implications. To bridge this gap between theory and reality, we introduce new formalizations to characterize new types of boundedly rational behavior that is missing in existing models but supported by experimental evidence. NLK, the first formalization we propose, is a new solution concept in Game Theory that connects two existing ones, Nash Equilibrium (NE) and Level-K model. Of these two, NE, introduced by 1994 Nobel Laureates John Nash has revolutionized the economics of Industrial Organization and has influenced many other branches such as the theories of monetary policy and international trade. However, there is mounting and robust evidence from laboratory experiments of substantial discrepancy between the predictions of NE and the behavior of players. Among all the alternative models that retain the individual rationality of optimization, but relax correct beliefs, Level-K model is probably the most prominent. Absent in NE, Level-K model explicitly allows players to consider their opponent as less sophisticated than themselves. But Level-K does not allow players to use ii an important element of strategic thinking, namely, “put yourself in the others’ shoes” and believe the opponent can think in the same way they do. Bridging NE and Level-K, NLK allows a player in a game to believe that her opponent may be either less- or as sophisticated as they—a view supported by various studies in Psychology. We compare the performance of NLK to that of NE and some versions of Level-K by applying it to data from three experimental papers published in top economics journals and to data from a field study. These studies allow us to test NLK on: (1). A static game of complete information, (2). A static game of incomplete information, (3). A dynamic game of perfect information, and (4). On field data. NLK provides additional insights to those of NE and Level-K. Moreover, a simple version of it explains the experimental data better in many cases. As a new solution concept, NLK shares a similar foundation to NE but is also applicable to games with players of different cognitive or reasoning abilities. As an analytical tool, NLK exists and gives a sharp prediction in general, and therefore it can be applied to empirical analysis in a broad range of settings. In the second formalization, we first propose two alternative axiomatic approaches, formalizing a distinct anomaly in hypothetical reasoning that agents fail to reason state-by- state. Our theory expands the foundation of Decision Theory and ties together a broad range of evidence documented in multiple disciplines that decision makers often choose a dominated strategy. Secondly, we extend our concept to Game Theory and Mechanism Design, where we identify a rich class of mechanisms that successfully achieve desirable goals even with boundedly rational agents and agents who mistrust the market makers. iii Thirdly, we test and verify our theory and its implications, by two laboratory experiments with a cross-over design that enables pooled data, within-subject, and cross-subject comparisons. Finally, we address how our approach contributes to accomplishing two goals simultaneously in modeling bounded rationality: providing a unified framework that subsumes existing ones as limiting cases and stimulating transdisciplinary conversations connecting the concepts of heuristics and emotions in Psychology, the utilization of eye- tracking technology in Neuroscience, and considerations of the moral foundation underlying a mechanism design in Ethics. The general insights of our work can be transferred to practical impacts on applications of Mechanism Design. Among these applications are the U.S. Federal Communications Commission auctions that raise more than 10 billion dollars yearly in government revenue; College Admissions that affect more than 10 million students every year around the world; and a Kidney Exchange Program with more than 1 million people waiting for kidney transplants. By formalizing bounded rationality into economic theory, our study honors the elegance of classic economic theory; at the same time, by modeling human behavior even more closely, it directs us to a new way of improving human welfare. In the history of economic thought lies a dilemma for future economists: should we adopt simple models with unrealistic assumptions, or should we describe human behavior closely but give up elegant abstractions? In the projects above, we endeavor to create a middle way that synthesizes the merits in both directions and leave unanswered questions for future researchers. iv Dedication The Master said, “Virtue is not left to stand alone. He who practices it will have neighbors.” —Analects, 4:25 I dedicate my dissertation to all the fools who yet hold on to their dream, bravely strive against adversity, and seek after coordination between theory and reality. As your sentiments resonate with mine, my joy expands. v Acknowledgments I am grateful for Prof. Ariel Rubinstein’s inspiration on formal modeling of bounded rationality, in general, and its application to mechanism design, in particular. Special thanks go to Prof. Dan Levin for his tireless mentoring and steadfast support during my entire Ph.D. journey. Chapter 1 of this dissertation is developed from his original idea and based on our joint work. I am indebted to Prof. Shengwu Li for his initial and insightful idea of Obvious Strategy-proof Mechanisms. Chapter 2 and 3 are closely related to and inspired by his work. I especially thank my dissertation adviser Prof. James Peck and Prof. Paul J. Healy on my committee for their careful, patient, and instructive guide to the completion of this work. I likewise want to show gratitude to Profs. Hal Arkes, Yaron Azrieli, Pierpaolo Battigali, John Kagel, Philippe Jehiel, Ian Krajbich, Ran Shorrer and Marciano Siniscalchi for their invaluable comments on the contents of this dissertation and much more. Although, all errors are my own and should not tarnish the reputations of these esteemed scholars. I have benefited from the comments of participants in the Texas Experimental Economic Symposium 2015, the Midwest Economic Theory and Trade Conference 2015, the D-TEA workshop 2015, the Summer School of the Econometric Society 2015 and 2016, ASSA meeting 2017, the 28th Stony Brook International Conference on Game Theory 2017, and the 70th European Meeting of the Econometric Society 2017. This work is supported in part by the JMCB Research Grant for Graduate vi Students and the NSF Dissertation Grant. Last but not the least, I am grateful for all the friends who show their support during my dark days. Among them, I especially thank my parents for their meticulous caring, Michelle Chapman, Prof. Hajime Miyazaki, and Rick Tobin for their assistance in administrative issues, Prof. Gary Charness and Prof. Chun-Lei Yang for their enlightening insights and practical guidance that raise me up in desperation, and Prof. Chongsheng Yu for offering me joy of mutual empathy by striving in a similar way. vii Vita Education Jun. 2012………………………………….B.A. Economics, Peking University Jun. 2012………………………………….B.S. Mathematics, Peking University Aug. 2013…………………………………M.A. Economics, The Ohio State University Apr. 2016…………………………………Ph.D. Candidate in Economics, The Ohio State University Fellowships/Scholarships Presidential Fellowship, Ohio State University, Summer 2017–Autumn 2018 Scholarship of I.S.E.O. Summer School Featuring Three Nobel Laureates, Apr. 2017 JMCB Fellowship, Department of Economics, The Ohio State University, 2012–2013 Scholarship of the KoGuan Chinese Rule of Law and Principle Studies Center, Mar. 2012 China National Scholarship, Peking University, 2010–2011 Scholarship of the Leo KoGuan Foundation, U.S.A, Peking University, 2009–2010 The May 4th Scholarship, Peking University, 2008–2009 Awards and honors viii L. Edwin Smart Graduate Associate Teaching Award, Department of Economics, The Ohio State University, Sep. 2016 L. Edwin Smart Departmental Citation for Excellence in Teaching, Department of Economics, The Ohio State University, Sep. 2015 Outstanding first-class Award for Undergraduate Dissertations, National School of Development and China Center for Economic Research, May. 2013 Outstanding Graduates, Beijing Municipal Commission of Education, Jun. 2012 Outstanding Graduates, Peking University, May 2012 A pacemaker to Merit Student, Peking University, 2010–2011 Merit Student, Peking University, 2009–2010 Grants National Science Foundation Research Grant for Doctoral Dissertation ($15,400), December 2016 Career Development Grant, OSU Council of Graduate Student, Fall 2016 Decision Science Collaborative Research Grant ($3000, with James Wei Chen), Fall 2016 JMCB Grant