Limits to Reputations

Much of the interest in the adverse selection approach to reputations in repeated games arises from the fact that quite small departures from the complete information model seems to have large effects on the set of equilibrium payoffs. We show that this is not the case in reputation games where a long-run player plays a fixed stage-game against an infinite sequence of short-run players under imperfect public-monitoring. We conclude that in such games, introducing arbitrarily small incomplete information cannot open the possibility of new equilibrium payoffs that are far away from the complete information equilibrium payoff set, even when the long-run player's discount factor is very high but fixed. Our main result implies that the standard reputation results hold true due to a specific order of limits.