THE KERNEL AND BARGAINING SET FOR CONVEX GAMES
HEBREW UNIV JERUSALEM (ISRAEL) DEPT OF MATHEMATICS
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Many solution concepts for cooperative games agree or partially agree if the game happens to be convex. For example, convex games have a unique von- Neumann Morgenstern solution which coincides with the core. Also, the Shapley value is a center of gravity of the extreme points of the core of a convex game namely, the center of gravity when the extreme points are assigned appropriate multiplicities. It is proved in this paper that the kernel for the grand coalition of a convex game lies in the relative interior of its core and that the bargaining set for the grand coalition coincides with the core.
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