Some Thoughts on the Theory of Cooperative Games

by Gerhard Jentzsch

Edited by Robert J. Aumann


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The result of an attempt to generalize the von Neumann-Morgenstern theory of n-person games by elimination the requirement that the utility functions be linear, or, more generally, by eliminating side payments altogether. Unless suitable restrictions are imposed, the minimax theorem for coalitions will not hold: outcomes will exist that can be neither guaranteed by a coalition nor prevented by the opposing coalition. The author broadens the class of games considered by von Neumann and Morgenstern while retaining the minimax property for coalitions. His chief result, as applied to games with side payments, is that each coalition must have a kind of "social utility function" for money.

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