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\(n\)-person games in partition function form. (English) Zbl 0229.90056

Summary: This paper gives a formulation of a theory of \(n\)-person cooperative games with side payments in terms of a partition function which is defined on the set of all partitions of the set of players. The results for all games with \(n\geq 3\) are presented. This development generalizes the von Neumann-Morgenstern theory of games in characteristic function form.

MSC:

91A06 \(n\)-person games, \(n>2\)
91A12 Cooperative games
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[1] ”On Solutions to n-Person Games in Partition Function Form,” Ph. D. thesis at The University of Michigan, Ann Arbor, 1963.
[2] and , Games and Decisions: Introduction and Critical Survey (John Wiley and Sons, Inc., New York, 1957). · Zbl 0084.15704
[3] ”Open Questions,” Dittoed paper presented at Princeton University Conference, 1953.
[4] ”Generalized characteristic functions for n-person games,” Proceedings of the Princeton University Conference of October 1961, privately printed for members of the conference, 1962, pp. 157–160.
[5] and , editors, Contributions to the Theory of Games, Volume N, Annals of Mathematics Studies, Number 40 (Princeton University Press, Princeton, 1959).
[6] and , Theory of Games and Economic Behavior (Princeton University Press, Princeton, 1953), 3d ed.
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