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.

I won't post it as an answer because I haven't read the paper, but it looks like this could be what you are after: http://www.sciencedirect.com/science/article/pii/S0899825612001285. It's in GEB, so it should be pretty decent. — Ubiquitous, Nov 21 '14 at 14:01
@Ubiquitous Thanks! It wasn't really exactly what I was thinking about (as it includes communication and incomplete information about the actions), but it would be a good answer non the less. In addition there are some references in there that look like they could be what I am looking for. — The Almighty Bob, Nov 21 '14 at 14:27
In this stage its critical to get answers, so it would be better if you posted it as such. — han-tyumi, Nov 22 '14 at 15:40
@Ubiquitous your comment lead to an answer, do you want to make an answer out of it? Otherwise I will write one as soon as I have the time. — The Almighty Bob, Nov 26 '14 at 09:25
@TheAlmightyBob Now might be a good time to make it into an answer. — Mathematician, Jan 30 '15 at 20:48

The Almighty Bob · Accepted Answer · 2015-08-08T19:27:13.997

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.

Is there a folk theorem for repeated games on networks?

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