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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.

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    $\begingroup$ 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: sciencedirect.com/science/article/pii/S0899825612001285. It's in GEB, so it should be pretty decent. $\endgroup$ – Ubiquitous Nov 21 '14 at 14:01
  • $\begingroup$ @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. $\endgroup$ – The Almighty Bob Nov 21 '14 at 14:27
  • $\begingroup$ In this stage its critical to get answers, so it would be better if you posted it as such. $\endgroup$ – han-tyumi Nov 22 '14 at 15:40
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    $\begingroup$ @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. $\endgroup$ – The Almighty Bob Nov 26 '14 at 9:25
  • $\begingroup$ @TheAlmightyBob Now might be a good time to make it into an answer. $\endgroup$ – Mathematician Jan 30 '15 at 20:48
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Yes, there are folk theorems for games on networks, depending on information structure and possible communication. Here are some of the most relevant papers:

Thanks @Ubiquitous for basically providing the answer.

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