On Continuity of Equilibrium Payoff Set in Repeated Games with Incomplete Information under Imperfect Public Monitoring

We study the equilibrium payoffs of a long-run player who plays a fixed-stage game of imperfect public monitoring against an infinite sequence of opponents each of whom plays only once. We show that for any d < 1, there exists an ? > 0 such that if in the repeated game where player 1's discount factor is d and the probability with which she is a commitment type is less than ?, long-run player's any equilibrium payoff is close to some equilibrium payoff in the complete information version of the repeated game. This means that under imperfect public monitoring, introducing arbitrarily small incomplete information cannot open the possibility of equilibrium payoffs for the long-run player that are far away from the complete information equilibrium payoff set.