On ordinal equivalence of the Shapley and Banzhaf values for cooperative games

On ordinal equivalence of the Shapley and Banzhaf values for cooperative games

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Article ID: iaor20106862
Volume: 39
Issue: 4
Start Page Number: 513
End Page Number: 527
Publication Date: Oct 2010
Journal: International Journal of Game Theory
Authors:
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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