The γ-Core and Coalition Formation

This paper reinterprets the ? -core (Chander and Tulkens (1995, 1997)) and justifies it as well as its prediction that the efficient coalition structure is stable in terms of the coalition formation theory. It is assumed that coalitions can freely merge or break apart, are farsighted (that is, it is the final and not the immediate payoffs that matter to the coalitions) and a coalition may deviate if and only if it stands to gain from it. It is then shown that subsequent to a deviation by a coalition, the nonmembers will have incentives to break apart into singletons, as is assumed in the definition of the ? - characteristic function, and that the grand coalition is the only stable coalition structure.