The Folk Theorem with Imperfect Public Information

Abstract

The Folk Theorem obtains in repeated games with imperfect public information if for each pair of agents there is at least one action profile where the information revealed by the publicly observed outcome permits deviations by one of the agents to be statistically distinguished from deviations by the other, and the dimension of the set of feasible payoffs equals the number of players.Under somewhat stronger conditions, we obtain a Folk Theorem for strict equilibria.Without pairwise full rank, a "Nash-threats" Folk Theorem obtains if the observed outcomes statisticallygive independent information about each player's actions.We give applications of our results to repeated agency models, the Green-Porter oligopoly model and repeated mechanism design.