We present a repeated prisoners' dilemma game with imperfect public monitoring, which exhibits the following paradoxical feature: the equilibrium payoff set expands and asymptotically achieves full efficiency as the public signal becomes less sensitive to the hiden actions of the players.

In the standard model of dynamic interaction, players are assumed to receive public signals according to some exogenous distributions for free. We deviate from this assumption in two directions to consider an aspect of information structure in a more realistic way. We assume that signals are...