A Nash Threats Folk Theorem for Repeated Games with Local Monitoring

We study sequential equilibrium payoffs of a repeated game with local interaction and local monitoring. An undirected network determines both the interaction and the monitoring structure. When players do not discount the future, a sequentially rational Nash threats folk theorem holds without any restrictions on the network structure. To prove this result, we construct strategies that support as a sequential equilibrium any payoff vector which is a convex combination (with rational weights) of stage game payoffs and is such that each player is strictly better off than under a Nash equilibrium of the stage game. No form of communication or coordination device is required. On the other hand, when players discount the future, the folk theorem cannot hold in our setting unless further restrictions are made either on payoffs or the network structure