Reputation in the presence of noisy exogenous learning

This paper studies the reputation effect in which a long-lived player faces a sequence of uninformed short-lived players and the uninformed players receive informative but noisy exogenous signals about the type of the long-lived player. We provide an explicit lower bound on all Nash equilibrium payoffs of the longlived player. The lower bound shows when the exogenous signals are sufficiently noisy and the long-lived player is patient, he can be assured of a payoff strictly higher than his minmax payoff.