Enlarged cores and bargaining schemes in games with fuzzy coalitions

In this paper we introduce a new concept of solution for games with fuzzy coalitions, which we call an enlarged core. The enlarged core captures an idea that various groups of fuzzy coalitions can have different bargaining power or influence on the final distribution of wealth resulting from the cooperation process. We study a bargaining scheme for the enlarged core, which is an iterative procedure for generating sequences converging to elements of the enlarged core. It is shown that the enlarged core coincides with Aubin's core for a specific class of games with fuzzy coalitions.