Reputation and the Flow of Information in Repeated Games

Abstract

Equilibrium payoff bounds from reputation effects are derived for repeated games with imperfect public monitoring in which a long‐run player interacts frequently with a population of short‐run players and the monitoring technology scales with the length of the period of interaction. The bounds depend on the monitoring technology through the flow of information, a measure of signal informativeness per unit of time based on relative entropy. Examples are shown where, under complete information, the set of equilibrium payoffs of the long‐run player converges, as the period length tends to zero, to the set of static equilibrium payoffs, whereas when the game is perturbed by a small ex ante probability on commitment types, reputation effects remain powerful in the high‐frequency limit.