Communication in Repeated Network Games with Private Monitoring∗

I consider repeated games with private monitoring played on a social network. Each player has a set of neighbors with whom he interacts: a player’s payoff depends on his own and his neighbors’ actions only. Monitoring is private and imperfect: each player observes his stage payoff but not his neighbors’ actions. I introduce costless communication among players at each stage: communication can be public, private or a mixture of both. I prove that a folk theorem holds for a large class of payoff functions if and only if any two players have a non-common neighbor.