Automorphisms and weighted values

The notion of automorphism is an essential tool to capture the meaning of any mathematical structure. The authors 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.