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Relation between the Shapley value and null group cohomology

Published online by Cambridge University Press:  17 April 2009

Andrzej Madrecki
Andrzej Madrecki
Affiliation:
Institute of Mathematics, Technical University of Wrocław, 50–370 Wrocław, Wvbrzeże Wyspiańskiego 27, Poland.
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Abstract

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The purpose of this paper is to give an application of homological methods to game theory. The main theorems give conditions of a homological nature for the existence and uniqueness of the Shapley value for games with continuum players.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 28 , Issue 2 , October 1983 , pp. 187 - 197
Copyright
Copyright © Australian Mathematical Society 1983

References

[1] Aumann, R.J. and Shapley, L.S., Values of non-atomic games (Princeton University Press, Princeton, New Jersey, 1974).Google Scholar
[2] Cartan, Henry and Eilenberg, Samuel, Homological algebra (Princeton University Series, 19. Princeton University Press, Princeton, New Jersey, 1956).Google Scholar
[3] Shapley, L.S., “A value for n-person games”, Contributions to the theory of games, Volume II, 301–317 (Annals of Mathematics Studies, 28. Princeton University Press, Princeton, New Jersey, 1953).Google Scholar