The folk theorem for the prisoner's dilemma with endogenous private monitoring

Abstract

We study the repeated prisoner's dilemma with private monitoring under the assumption that the monitoring structure is endogenously chosen by the players in each period. We allow the players to choose from all possible monitoring structures. If the players disagree on the monitoring structure they would like, the realized monitoring structure is determined by a function that aggregates their choices. When one player can dictate the monitoring structure, then the repetition of the stage Nash is the only sequential equilibrium outcome. In contrast, when no player can dictate the monitoring structure, we provide conditions on the aggregation function under which any strictly individually rational and feasible payoff vector can be supported in sequential equilibrium.