Reputation in dynamic games

Abstract

We analyze reputation in a game between a large player and a continuum of long-lived small players in which state variables affect players' payoffs. The large player's type is private information. We give conditions under which in every Nash equilibrium a very patient large player will get almost the largest payoff consistent with the small players choosing a best response in a large finite truncation of the game. While our results apply to the time inconsistency problem of optimal government policy, we show that for the durable goods monopoly reputation may fail to improve the monopolist's payoff