Abstract
Four axioms, based on Shapley's original development of the Shapley value, are proposed for values of cooperative games with quarrelling. The collection of all values satisfying these axioms is shown to be the collection of values determined by a construction utilizing the proper choices of several parameters. This facilitates the proof of several common properties of all these values which are analogous to properties of the usual Shapley value. Finally, the parameters corresponding to the two specific values for games with quarrelling proposed in [2], are presented.
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Bibliography
Aumann, R. J. and Shapley, L. S., Values of Non-Atomic Games, Princeton University Press, Princeton, N.J., 1974.
Kilgour, D. M., ‘A Shapley value for Cooperative Games with Quarrelling’, in Game Theory as A Theory of Conflict Resolutions, (ed. by A. Rapoport), Reidel, Dordrecht, Holland, 1974, pp. 193–206.
Owen, G., Game Theory, Saunders, Philadelphia, 1968.
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, N. J., 1953, pp. 307–317.
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Kilgour, D.M. Axioms for Shapley values in games with quarrelling. Theor Decis 8, 193–207 (1977). https://doi.org/10.1007/BF00133411
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DOI: https://doi.org/10.1007/BF00133411