Reputation and Observability in Repeated Games with Equally Patient Players

Yale University, New Haven CT

Investigators

Abstract

This project concerns new research in the theory of reputation in repeated games, a branch of noncooperative game theory that has a wide range of applications in Economics, including to analysis of monopolistic practices, commitment in monetary policy, reputation in debt markets, credibility in information transmission and breakdown in credence good markets. The PI and his collaborator develop a new method to study reputation effects in two-player repeated games with equally patient players, imperfect monitoring and one-sided incomplete information. Recall that the reputation effect is the phenomenon that the patient limit of the set of equilibrium payoffs of a repeated game changes dramatically when the game is perturbed by small amounts of incomplete information in the form of an ex ante small probability that one of the players is committed to a given strategy. In the benchmark case in which a long-run player faces a sequence of myopic short-run players, it is well known that reputation effects select the Stackelberg payoff in the patient limit under fairly general conditions. This provides a foundation for the intuitive idea that "reputation substitutes for commitment." The case where both players are forward looking and comparably patient, while clearly important, is not nearly as well understood. Existing results show that reputation effects are elusive when players have equal discount factors and monitoring is perfect. The investigator and a collaborator propose a methodology to study the case in which there is imperfect public monitoring, that is, the players observe a noisy public signal about their actions. The methods are used to show that, unlike the perfect monitoring case, when the informed player is imperfectly monitored and the stage game has common interests (a class of games that includes well known models of nuclear disarmament and currency attacks), reputation effects select the Stackelberg payoff in the limit as the common discount factor tends to one.