Instability of Equilibria with Imperfect Private Monitoring

Various papers have presented folk-theorem results that yield efficiency in the repeated Prisoner's Dilemma with imperfect private monitoring. I present a mild equilibrium refinement that requires robustness against small perturbations in the behavior of potential opponents, and I show that only defection satisfies this mild refinement among all the equilibria in the existing literature, unless one assumes either (1) communication among the players, or (2) sufficient correlation between the private signals (conditional on the action-profile).