published in Econometrica, 64 (May 1996): 691-704.

Full Text

Maintaining a Reputation Against a Long-Lived Opponent

Marco Celentani, Drew Fudenberg, David K. Levine and Wolfgang Pesendorfer

April 8, 1995

revised: November 29, 1996

Abstract: We analyze reputation in a game between a patient player 1 and a non-myopic but less patient opponent, player 2. Player 1's type is private information and he may be a "commitment type" who is locked into playing a particular strategy. We assume that players do not directly observe each other's action but rather see an imperfect signal of it. In particular, we assume that the support of the distribution of signals is independent of how player 2 plays. We show that in any Nash equilibrium of the game player 1 will get a payoff close to the largest payoff consistent with player 2 choosing a best response in a finite truncation of the game. Moreover, we show that if the discount factor of player 2 is sufficiently large then player 1 will get approximately the maximum payoff consistent with player 2 getting at least his pure strategy minmax payoff .