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Vladimir_Nesov comments on indexical uncertainty and the Axiom of Independence - Less Wrong
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I couldn't find anything that "clicked" with cooperation in PD. Above, I wasn't talking about a kind of Nash equilibrium protected from coalition deviations. The correlated strategy needs to be a Pareto improvement over possible coalition strategies run by subsets of the agents, but it doesn't need to be stable in any sense. It can be strictly dominated, for example, by either individual or coalition deviations.
A core in Cooperative Game Theory doesn't have to be a Nash equilibrium. Take a PD game with payoffs (2,2) (-1,3) (3,-1) (0,0). In Cooperative Game Theory, (-1,3) and (3,-1) are not considered improvements that a player can make over (2,2) by acting for himself. Maybe one way to think about it is that there is an agreement phase, and an action phase, and the core is the set of agreements that no subset of players can improve upon by publicly going off (and forming their own agreement) during the agreement phase. Once an agreement is reached, there is no deviation allowed in the action phase.
Again, I'm just learning Cooperative Game Theory, but that's my understanding and it seems to correspond exactly to your concept.
Sounds interesting, thank you.