Reputation Effects Under Interdependent Values

A patient player privately observes a persistent state and interacts with an infinite sequence of myopic uninformed players. The patient player is either a strategic type who maximizes his payoff or one of several commitment types who mechanically play the same action in every period. I focus on situations in which the uninformed player's best reply to a commitment action depends on the state and where the total probability of commitment types is sufficiently small. I show that the patient player's equilibrium payoff is bounded below his commitment payoff in some equilibria under some of his payoff functions. This is because he faces a trade‐off between building his reputation for commitment and signaling favorable information about the state. When players' stage‐game payoff functions are monotone‐supermodular , the patient player receives high payoffs in all states and in all equilibria. Under an additional condition on the state distribution, my reputation model yields a unique prediction on the patient player's equilibrium payoff and on‐path behavior.