In repeated games with imperfect public monitoring, players can use public signals to coordinate their behavior perfectly, and thus support cooperative outcomes with the threat of punishments. But with even a small amount of private monitoring, players’ private histories may lead them to have suﬀiciently diﬀerent views of the world that such coordination on punishments is no longer possible (we describe a simple strategy proﬁle that is a perfect public equilibrium of a repeated prisoner’s dilemma with imperfect public monitoring, and yet is not an equilibrium for arbitrarily close games with private monitoring). If a perfect public equilibrium has players’ behavior conditioned only on ﬁnite histories, then it induces an equilibrium in all close-by games with private monitoring. This implies a folk theorem for repeated games with almost-public almost-perfect monitoring.
Mailath, George J. and Morris, Stephen, "Repeated Games with Almost-Public Monitoring" (1999). Cowles Foundation Discussion Papers. 1485.