Repeated games with local monitoring and private communication

•I study repeated games with private local monitoring and private communication.•At each stage, each player observes the moves of his neighbors.•At each stage, each player can communicate secretly with all players.•The solution concept is perfect Bayesian equilibrium.•A folk theorem holds if and only if each player has two neighbors.

I consider repeated games with local monitoring: each player observes his neighbors' moves only. Hence, monitoring is private and imperfect. Communication is private: each player can send different (costless) messages to different players. The solution concept is perfect Bayesian equilibrium. I prove that a folk theorem holds if and only if each player has two neighbors. This extends the result of Ben-Porath and Kahneman (1996) to private communication, provided the existence of sequential equilibrium.