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 preservingall weighted Shapley values.
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References
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Carreras' research supported by project UPV 036321-HA186/92 of the Basque Country University. Owen's research supported by the National Science Foundation, Grant DMS-9116416. This collaboration was made possible by the Polytechnic University of Catalonia, which sponsored Owen's visit to Terrassa.
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Carreras, F., Owen, G. Automorphisms and weighted values. Int J Game Theory 26, 1–10 (1997). https://doi.org/10.1007/BF01262508
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DOI: https://doi.org/10.1007/BF01262508