Notes on N-Person Games VII

Cores of Convex Games

by Lloyd S. Shapley

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The core of an [n]-person game is the set of outcomes that cannot be blocked by any coalition of players. The Memorandum demonstrates that the core of a convex game has an especially regular structure, and that it is closely related to two other solution concepts: (1) the value solution is the center of gravity of the extreme points of the core, and (2) the von Neumann-Morgenstern stable set solution is unique and coincides with the core.

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