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Nash equilibrium occurs when there is no benefit gained by changing its strategy unilaterally from the equilibrium strategy.

So is there any equilibrium named for the following case: when there is no benefit gained by changing one's strategy from equilibrium when everyone knows each other's strategies, and with consideration to everyone's strategy, there is no benefit that will be obtained.

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Can you state your question more clearly? –  Alexander Gruber Feb 4 '13 at 3:37
    
I recommend you have a look at Aumann's Interactive epistemology I: Knowledge in order to state your question more clearly.ma.huji.ac.il/raumann/pdf/Interactive%20epistemology1.pdf –  Metta World Peace Feb 4 '13 at 4:02

2 Answers 2

In the exact way you appear to describe it, a game in which, say, there is one matrix entry that is best for all players, this wouldn't be very interesting in a world of rational actors. However, there are coordination games, say, within cooperative game theory in which coordination among the players to achieve a mutually beneficial outcome among several mutually beneficial outcomes can be achieved. Have a look at http://en.m.wikipedia.org/wiki/Coordination_game. Maybe this covers some of what you were interested in. You are still typically looking at Nash equilibria though.

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I'm not sure I understand your question correctly though. Maybe you are thinking of something like common knowledge, en.m.wikipedia.org/wiki/Common_knowledge_(logic). –  gnometorule Feb 4 '13 at 3:50

If I understood your description. The reasoning you have given is already assumed in Nash equilibrium. That is to say, regarding the equilibrium concept of Nash, even though everybody knows everybody else's strategy nobody wants to deviate from her strategy in a Nash equilibrium. So there is no benefit for someone to change her strategy. Note that everybody knows that everybody knows that everybody is rational, i.e. common knowledge is common knowledge as well.

What is not assumed in Nash equilibrium is the following. It is not allowed for players to form coalitions. That is, two or more players can not act together to improve their payoff. But as you say "changing one's strategy" I do not think forming coalitions is what you mean. If so, then you can check "cooperative game theory".

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