Farsighted Coalitional Stability

I define the largest consistent set, a solution concept which applies to situations in which coalitions freely form but cannot make binding contracts, act publicly, and are fully ``farsighted'' in that a coalition considers the possibility that once it acts, another coalition might react, a third coalition might in turn react, and so on, without limit. I establish weak nonemptiness conditions and apply it to strategic and coalitional form games and majority rule voting. I argue that it improves on the von Neumann- Morgenstern stable set as it is usually defined but is consistent with a generalization of the stable set as in the theory of social situations.