Reputation in long-run relationships

Abstract

We model a long-run relationship as an infinitely repeated game played by two equally patient agents. In each period, the agents play an extensive-form stage game of perfect information with either locally non-conflicting interests or strictly conflicting interests. There is incomplete information about the type of Player 1, while Player 2's type is commonly known. We show that a sufficiently patient Player 1 can leverage Player 2's uncertainty about his type to secure his highest pay-off, compatible with Player 2's individual rationality, in any perfect Bayesian equilibrium of the repeated game.