Solutions of transferable utility cooperative games

A uniform competitive solution predicts a configuration of payoff vectors associated with coalitions which are likely to form in a cooperative game. This configuration satisfies the internal and external stability principles and the predicted payoffs are both individually and coalitionally rational. The uniform competitive solution is a modified version of the competitive solution concept introduced by R. D. McKelvey, P. C. Ordeshook and M. D. Winer. A parallel study of these two solution concepts emphasizes their common properties and the existing differences. Existence theorems of uniform competitive solutions are provided under very general assumptions and it is proved that competitive solutions exists only for some special classes of transferable utility games.