Essays on Dynamic Games and Reputations by Di Pei B.A. Mathematics, Tsinghua University (2011) M.A. Economics, Toulouse School of Economics (2013) Submitted to the Department of Economics in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Economics at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY June 2018 ○c Di Pei, MMXVIII. All rights reserved. The author hereby grants to MIT permission to reproduce and to distribute publicly paper and electronic copies of this thesis document in whole or in part in any medium now known or hereafter created. Author................................................................................... Department of Economics June 1, 2018 Certified by. Daron Acemoglu Elizabeth and James Killian Professor of Economics Thesis Supervisor Certified by. Drew Fudenberg Paul A. Samuelson Professor of Economics Thesis Supervisor Certified by. Juuso Toikka Gary Loveman Career Development Associate Professor of Economics Thesis Supervisor Accepted by.............................................................................. Ricardo Caballero Ford International Professor of Economics Chairman, Departmental Committee on Graduate Studies 2 Essays on Dynamic Games and Reputations by Di Pei Submitted to the Department of Economics on June 1, 2018, in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Economics Abstract This thesis consists of three essays on dynamic games with incomplete information. In Chapter 1, I study reputation effects when individuals have persistent private information that matters for their opponents' payoffs. I examine a repeated game between a patient informed player and a sequence of myopic uninformed players. The informed player privately observes a persistent state, and is either a strategic type who can flexibly choose his actions or is one of the several commitment types that mechanically plays the same action in every period. Unlike the canonical models on reputa- tion effects, the uninformed players' payoffs depend on the state. This interdependence of values introduces new challenges to reputation building, namely, the informed player could face a trade- off between establishing a reputation for commitment and signaling favorable information about the state. My results address the predictions on the informed player's payoff and behavior that apply across all Nash equilibria. When the stage game payoffs satisfy a monotone-supermodularity condition, I show that the informed long-run player can overcome the lack-of-commitment prob- lem and secure a high payoff in every state and in every equilibrium. Under a condition on the distribution over states, he will play the same action in every period and maintain his reputation for commitment in every equilibrium. If the payoff structure is unrestricted and the probability of commitment types is small, then the informed player's return to reputation building can be low and can provide a strict incentive to abandon his reputation. In Chapter 2, I study the dynamics of an agent's reputation for competence when the labor market's information about his performance is disclosed by an intermediary who cannot commit. I show that this game admits a unique Markov Perfect Equilibrium (MPE). When the agent is patient, his effort is inverse U-shaped, while the rate of information disclosure is decreasing over time. I illustrate the inefficiencies of the unique MPE by comparing it with the equilibrium in the benchmark scenario where the market automatically observes all breakthroughs. I characterize a tractable subclass of non-Markov Equilibria and explain why allowing players to coordinate on payoff-irrelevant events can improve efficiency on top of the unique MPE and the exogenous information benchmark. When the intermediary can commit, her optimal Markov disclosure policy has a deadline, after which no breakthrough will be disclosed. However, deadlines are not incentive compatible in the game without commitment, illustrating a time inconsistency problem faced by the intermediary. My model can be applied to professional service industries, such as law and consulting. My results provide an explanation to the observed wage and promotion patterns in Baker, Gibbs and Holmstr¨om(1994). In Chapter 3, I study repeated games in which a patient long-run player (e.g. a firm) wishes to win the trust of some myopic opponents (e.g. a sequence or a continuum of consumers) but has a strict incentive to betray them. Her benefit from betrayal is persistent over time and is her private information. I examine the extent to which persistent private information can overcome this lack-of-commitment problem. My main result characterizes the set of payoffs a patient long-run 3 player can attain in equilibrium. Interestingly, every type's highest equilibrium payoff only depends on her true benefit from betrayal and the lowest possible benefit in the support of her opponents' prior belief. When this lowest possible benefit vanishes, every type can approximately attain her Stackelberg commitment payoff. My finding provides a strategic foundation for the (mixed) Stackelberg commitment types in the reputation models, both in terms of the highest attainable payoff and in terms of the commitment behaviors. Compared to the existing approaches that rely on the existence of crazy types that are either irrational or have drastically different preferences, there is common knowledge of rationality in my model, and moreover, players' ordinal preferences over stage game outcomes are common knowledge. Thesis Supervisor: Daron Acemoglu Title: Elizabeth and James Killian Professor of Economics Thesis Supervisor: Drew Fudenberg Title: Paul A. Samuelson Professor of Economics Thesis Supervisor: Juuso Toikka Title: Gary Loveman Career Development Associate Professor of Economics 4 Acknowledgments I am deeply indebted to my advisors Drew Fudenberg, Daron Acemoglu and Juuso Toikka for their continuous guidance, encouragement and support in the past five years. I was fortunate enough to take Drew's game theory course at Harvard in my first year. His lectures stimulated my interests in repeated games and reputations, and more importantly, equipped me with the technical tools to do frontier research in economic theory. Drew became the natural choice for my primary advisor after I decided to write my job market paper on reputation effects. I was constantly impressed by the sharpness of his mind, the clarity of his thinking and the speed with which he learns new things. Drew has always been approachable to graduate students and enjoys a reputation for being generous with his time and belongings. Every time I emailed him a 10-page proof I wrote, he would always get back to me within half an hour with very detailed comments. I also appreciate his continuous investments into the Harvard-MIT theory community, by, for example, running weekly theory reading groups, inviting Harvard students to present in the MIT theory lunch, hosting annual theory parties in his house, etc. My story with Daron started after finishing my general exams. I emailed him in June and asked for a summer RAship. He happily agreed and we started talking several potential applications of mechanism design to political economy problems, which eventually developed into a coauthored paper on constitutional design. Daron is the one of the broadest economists I have ever met: the conversations in his office could start from a discussion on some deep mathematical theorems and end with mapping the results I just obtained to features in the Bill of Rights or the Peloponnesian War. Every discussion with Daron is an invaluable experience. I learnt a lot in terms of how to ask an economically interesting question, how to abstract a complicated economic problem into a simple model and how to justify the economic significance of the results being derived. Juuso has always been my hero, both as an economic theorist and as a teacher/advisor. He is a deep thinker, very rigorous in stating theorems and writing proofs, yet at the same time, being accessible and has the talent of explaining deep theoretical ideas in intuitive and non-technical ways. I was lucky enough to be his teaching assistant in contract theory for three consecutive years, from which I learnt a lot on how to give good lectures and clear presentations. We spent hours in his office, going through the modeling assumptions and the proof techniques of nearly every project I have attempted in graduate school, no matter whether it has eventually turned into a paper or not. I have always admired his dedication to scientific research, his colleagues, his students and his family, and I hope I could follow his example after starting my job at Northwestern University. I would also like to thank Christian Hellwig, Jean Tirole, Robert Gibbons and Alexander Wolitzky, who have all been instrumental in helping me grow as an economist. I would definitely not be in this position had it not been for Christian and Jean, my advisors in Toulouse. They introduced me to research in economics, showed me how to become a good scholar and had given me numerous advice on how to write papers, how to give talks, how to get along with colleagues, etc. Bob is a great mentor and has always been my first choice whenever I am seeking for career advice. He was always open to discussing research ideas even when it became clear that I was not on the path to becoming an organizational economist. In my opinion, Alex is one of the best and most productive theorists in his generation, yet at