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

<ul>
<li>Ben-Porath, E., &amp; Kahneman, M. (1996). <a href="http://www.sciencedirect.com/science/article/pii/S0022053196900903" rel="noreferrer">Communication in repeated
games with private monitoring</a>. Journal of Economic Theory, 70(2),
281-297. - <em>public communication, private monitoring</em></li>
<li>Renault, J., &amp; Tomala, T. (1998). <a href="http://link.springer.com/article/10.1007/s001820050089" rel="noreferrer">Repeated proximity games</a>.
International Journal of Game Theory, 27(4), 539-559. - <em>complete information, imperfect monitoring</em></li>
<li>Tomala, T. (2011). <a href="http://pubsonline.informs.org/doi/abs/10.1287/opre.1110.0936" rel="noreferrer">Fault reporting in partially known networks and
folk theorems</a>. Operations research, 59(3), 754-763. - <em>partial knowledge of the network and restricted communication</em></li>
<li>Laclau, M. (2012). <a href="http://www.sciencedirect.com/science/article/pii/S0899825612001285" rel="noreferrer">A folk theorem for repeated games played on a
network</a>. Games and Economic Behavior, 76(2), 711-737. - <em>private communication</em></li>
</ul>

<p>Thanks @Ubiquitous for basically providing the answer.</p>

CC BY-SA 3.0
2015-03-27T08:47:16.567Z
2015-08-08T19:27:13.997Z
2015-08-08T19:27:13.997Z
The Almighty Bob
<p>Games on networks have been studied extensively, however, I was not able to find a <a href="http://en.wikipedia.org/wiki/Folk_theorem_%28game_theory%29">folk theorem</a> for games on networks. Is there one or can it be derived from an already existing folk theorem?</p>

<p>With <strong>games on networks</strong> 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.</p>

CC BY-SA 3.0
2014-11-26T09:25:04.233Z
@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
CC BY-SA 3.0
2015-01-30T20:48:21.723Z
@TheAlmightyBob Now might be a good time to make it into an answer.
Mathematician
CC BY-SA 3.0
2014-11-21T14:01:50.700Z
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
CC BY-SA 3.0
2014-11-21T14:27:30.803Z
@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
CC BY-SA 3.0
2014-11-22T15:40:17.797Z
In this stage its critical to get answers, so it would be better if you posted it as such.
han-tyumi
<game-theory><reference-request><networks>
Is there a folk theorem for repeated games on networks?
The Almighty Bob
# Is there a folk theorem for repeated games on networks?

(Asked by: username_0 on 2014-11-21)

Games on networks have been studied extensively, however, I was not able to find a [folk theorem](http://en.wikipedia.org/wiki/Folk_theorem_%28game_theory%29) 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.

**Tags:** game-theory, reference-request, networks
> **Comments:**
> **username_2**: 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.  
> **username_0**: @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.  
> **username_3**: In this stage its critical to get answers, so it would be better if you posted it as such.  
> **username_0**: @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.  
> **username_1**: @TheAlmightyBob Now might be a good time to make it into an answer.  

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## 1 answers

### Answer by username_0 on 2015-03-27. Score: 8 | Accepted answer

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](http://www.sciencedirect.com/science/article/pii/S0022053196900903). Journal of Economic Theory, 70(2),
  281-297. - *public communication, private monitoring*
* Renault, J., & Tomala, T. (1998). [Repeated proximity games](http://link.springer.com/article/10.1007/s001820050089).
  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](http://pubsonline.informs.org/doi/abs/10.1287/opre.1110.0936). 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](http://www.sciencedirect.com/science/article/pii/S0899825612001285). Games and Economic Behavior, 76(2), 711-737. - *private communication*

Thanks @Ubiquitous for basically providing the answer.


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