Less is more: an observability paradox in repeated games

We present a repeated prisoners’ dilemma game with imperfect public monitoring, which exhibits the following paradoxical feature: the (limit) equilibrium payoff set achieves full efficiency asymptotically as the public signal becomes insensitive to the hidden actions of the players. The basic logic behind this result also provides an example where the Folk theorem is obtained, while Fudenberg-Levine-Maskin’s sufficient conditions (Econometrica 1994) for Folk theorem are violated.