Abstract
The Shapley value [1] has proven to be a useful evaluation of a player’s strategic position in an essential cooperative game. In this paper, we shall consider two extensions of the Shapley value to games in which there is a set of players, each of whom refuses to join any coalition already containing another player in the set. Such an extension will provide information about the strategic value of cooperation in the game. For example, by subtracting a quarreller’s extended Shapley value from his extended Shapley value when he is removed from the set of quarrellers, we determine the value to him of cooperation with the other quarrellers. Similarly, we can find the value to any player of cooperation among the quarrellers (if it were possible).
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Bibliography
Shapley, L. S.,‘A Value for n-Person Games’, in Contributions to the Theory of Games, Vol. II (ed. by H. W. Kuhn and A. E. Tucker), Princeton University Press, Princeton, N.J., 1953, pp. 307–317.
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© 1974 D. Rediel Publishing Company, Dordrecht, Holland
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Kilgour, D.M. (1974). A Shapley Value for Cooperative Games with Quarrelling. In: Rapoport, A. (eds) Game Theory as a Theory of a Conflict Resolution. Theory and Decision Library, vol 2. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-2161-6_9
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DOI: https://doi.org/10.1007/978-94-010-2161-6_9
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-277-0489-4
Online ISBN: 978-94-010-2161-6
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