Reputation in the Presence of Noisy Exogenous Learning

Abstract

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 long-lived 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.