GENERALIZED CORES AND STABLE SETS FOR FUZZY GAMES

Core elements (a la Aubin) of a fuzzy game can be associated with additive separable supporting functions of fuzzy games. Generalized cores whose elements consist of more general separable supporting functions of the game are introduced and studied. While the Aubin core of unanimity games can be empty, the generalized core of unanimity games is nonempty. Properties of the generalized cores and their relations to stable sets are studied. For convex fuzzy games interesting properties are found such as the fact that the generalized core is a unique generalized stable set.