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