Efficiency in Repeated Games Revisited: The Role of Private Strategies∗

Most theoretical or applied research on repeated games with imperfect monitoring has restricted attention to public strategies ; strategies that only depend on history of publicly observable signals, and perfect public equilibria (PPE); sequential equilibria in public strategies. The present paper sheds light on the role of private strategies ; strategies that depend on players’ own actions in the past as well as observed public signals. Our main finding is that players can sometimes make better use of information by using private strategies and efficiency in repeated games can often be drastically improved. We illustrate this for games with a small signal space, where the Folk Theorem fails, as well as for games with a large signal space, for which the Folk Theorem holds. Our private strategy consists of two states and has the property that the opponent’s incentives are independnt of the state the player is in. We provide two different characterizations of our two-state equilibrium for general two-person repeated games with imperfect public monitoring.