A belief-based approach to the repeated prisoners' dilemma with asymmetric private monitoring

The belief-based approach for repeated games with private monitoring studies an important class of strategies where at each point of the game, each player’s optimal continuation strategy is determined by the player’s beliefs of the private state of the opponents. This paper extends the belief-based approach to the repeated prisoners’dilemma with asymmetric private monitoring. We …rst …nd that the previous belief-based techniques (Sekiguchi (1997), Bhaskar and Obara (2002)) for the repeated prisoners’dilemma cannot succeed when players’ private monitoring technologies are very di¤erent. We then modify the previous belief-based strategies by letting the player with smaller observation errors always randomize between cooperate and defect along the cooperative path of the play. It is shown that full e¢ ciency can be approximated and a full folk theorem can be obtained using our modi…ed belief-based strategies, provided that observation errors are small enough. We further construct a complete example to show that our belief-based strategies can be potentially generalized to other repeated games with almost-perfect private monitoring. JEL Classi…cation: C72, C73, D82.