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.