How robust is the folk theorem?

The folk theorem of repeated games has established that cooperative behavior can be sustained as an equilibrium in repeated settings. Early papers on private monitoring and a recent paper of Cole and Kocherlakota (Games and Economic Behavior, 53 [2005], 59-72) challenge the robustness of this result by providing examples in which cooperation breaks down when players observe only imperfect private signals about other players' actions, or when attention is restricted to strategies with finite memory. This paper shows that Cole and Kocherlakota's result is an artefact of a further restriction that they impose. We prove that the folk theorem with imperfect public monitoring holds with strategies with finite memory. As a corollary, we establish that the folk theorem extends to environments in which monitoring is close to public, yet private.