Automorphisms and Weighted Values

Guillermo Owen and Francesc Carreras
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Guillermo Owen: Department of Mathematics, Naval Postgraduate School, Monterey, CA 93943, USA
Francesc Carreras: Department of Applied Mathematics, School of Industrial Engineering, P.O. Box 577, 08220 Terrassa, Barcelona, Spain

International Journal of Game Theory, 1997, vol. 26, issue 1, 10 pages

Abstract: The notion of automorphism is an essential tool to capture the meaning of any mathematical structure. We apply this idea to cooperative games and obtain two interesting characterizations of the automorphisms of such a game: the one, in the complete case, as the permutations of players which preserve the (classical) Shapley value; the other, for the general case, as the permutations preserving all weighted Shapley values.

Date: 1998-05-19
Note: Received August 1993 Revised version September 1994
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