Is there a folk theorem for repeated games on networks?

Question

Games on networks have been studied extensively, however, I was not able to find a folk theorem for games on networks. Is there one or can it be derived from an already existing folk theorem?

With games on networks I mean games in which the payoff of the stage game only depends on the actions of the direct neighbors in a network. Simple examples for that would be the the majority game (in which the payoff depends on the number of neighbors that play the same action as you are) or a prisoner's dilemma played with each neighbor.

Answer 1

Yes, there are folk theorems for games on networks, depending on information structure and possible communication. Here are some of the most relevant papers:

• Ben-Porath, E., & Kahneman, M. (1996). Communication in repeated games with private monitoring. Journal of Economic Theory, 70(2), 281-297. - public communication, private monitoring
• Renault, J., & Tomala, T. (1998). Repeated proximity games. International Journal of Game Theory, 27(4), 539-559. - complete information, imperfect monitoring
• Tomala, T. (2011). Fault reporting in partially known networks and folk theorems. Operations research, 59(3), 754-763. - partial knowledge of the network and restricted communication
• Laclau, M. (2012). A folk theorem for repeated games played on a network. Games and Economic Behavior, 76(2), 711-737. - private communication

Thanks @Ubiquitous for basically providing the answer.