Reputation Effects under Short Memories

Abstract

I analyze a reputation game between a patient player and a sequence of short-run players. Each short-run player observes the number of times that the patient player took each of his actions in the past K periods. When players have monotone supermodular payoffs, the patient player can approximately secure his commitment payoff in all equilibria regardless of K . I also show that the short-run players can approximately attain their highest feasible payoff in all equilibria if and only if K is lower than some cutoff. This is because a larger K weakens the short-run players’ incentives to punish the patient player.