Is there a folk theorem for repeated games on networks? 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.
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., &amp; Kahneman, M. (1996). Communication in repeated
games with private monitoring. Journal of Economic Theory, 70(2),
281-297. - public communication, private monitoring
Renault, J., &amp; 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.