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Cores of convex games. (English) Zbl 0222.90054
In game theory, a convex game is one in which the incentives for joining a coalition increase as the coalition grows. This paper shows that the core of such a game – the set of outcomes that cannot be improved on by any coalition of players, is quite large and has an especially regular structure. Certain other cooperative solution concepts are shown to be related to the core in simple ways:
(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. (Similar results for (3) the kernel and (4) the bargaining set will be presented in a later paper.)
It is also shown that a convex game is not necessarily the sum of any number of convex measure games, and that the convex game is decomposable if and only if its core has less than full dimension.
Reviewer: Shapley, Lloyd S.

MSC:
91A12 Cooperative games
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