Essays on Reputations and Dynamic Games

This dissertation consists of three essays on reputations and dynamic games. I investigate how incomplete information, Bayesian Learning and strategic behavior interplay in different dynamic settings. In Chapter 1, I study reputation effects between a long-lived seller and different short-lived buyers where buyers enter the market at random times and only observe a coarse public signal about past transactions. The signal measures the difference between the number of good and bad outcomes in a biased way: a good outcome is more likely to increase the signal than a bad outcome to decrease it. The seller has a short-run incentive to shirk, but makes high profits if it were possible to commit to high effort. I show if there is a small but positive chance that the seller is a commitment type who always exerts high effort and if information bias is large, equilibrium behavior of the seller exhibits cyclic reputation building and milking. The seller exerts high effort at some values of the signals in order to increase the chance of reaching a higher signal and build reputation. Once the seller builds up his reputation through reaching a high enough signal, he exploits it by shirking. In chapter 2, I study the reputation effect in which a long-lived player faces a sequence of uninformed short-lived players and the uninformed players receive informative but noisy exogenous signals about the type of the long-lived player. I provide an explicit lower bound on all Nash equilibrium payoffs of the long-lived player. The lower bound shows when the exogenous signals are sufficiently noisy and the long-lived player is patient, he can be assured of a payoff strictly higher than his minmax payoff. In Chapter 3 I study optimal dynamic monopoly pricing when a monopolist sells a product with unknown quality to a sequence of short-lived buyers who have private information about the quality. Because past prices and buyers’ purchase behavior convey information about private signals, they jointly determine the public belief about the quality of the monopolist’s product. The monopolist is essentially doing experimentation in the market because every price charged generates not only current period profit but also additional information about the quality. I focus on information structures with a continuum of signals. Under a mild regularity condition on information structures, I show that in equilibrium, the optimal price is an increasing function of the public beliefs. In addition, I fully characterize information cascade sets in terms of information structure. I find that the standard characterization in terms of boundedness of information structure in the social learning literature no longer holds in the presence of a monopoly. In fact, whether herding occurs or not depends more on the values of the conditional densities of the signals at the lowest signal