On ordinal equivalence of the Shapley and Banzhaf values for cooperative games |
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Authors: | Josep Freixas |
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Institution: | 1. Department of Applied Mathematics III, Engineering School of Manresa, Technical University of Catalonia, EPSEM, Av. Bases de Manresa, 61–73, 08242, Manresa, Spain
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Abstract: | In this paper I consider the ordinal equivalence of the Shapley and Banzhaf values for TU cooperative games, i.e., cooperative games for which the preorderings on the set
of players induced by these two values coincide. To this end I consider several solution concepts within semivalues and introduce
three subclasses of games which are called, respectively, weakly complete, semicoherent and coherent cooperative games. A
characterization theorem in terms of the ordinal equivalence of some semivalues is given for each of these three classes of
cooperative games. In particular, the Shapley and Banzhaf values as well as the segment of semivalues they limit are ordinally
equivalent for weakly complete, semicoherent and coherent cooperative games. |
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