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

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 .