Local Communication in Repeated Games with Local Monitoring

I consider repeated games with local monitoring: each player observes his neighbors' moves only. Hence, monitoring is private and imperfect. I assume local and public communication: communication is restricted to neighbors, and each player sends the same message to each of his neighbors at each stage. Both communication and monitoring structures are given by the network. The solution concept is perfect Bayesian equilibrium. In the four-player case, a folk theorem holds if and only if the network is 2-connected. Some examples are given for games with more than four players