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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.
CitationFreixas, J. On ordinal equivalence of the Shapley and Banzhaf values for cooperative games. "International journal of game theory", Setembre 2010, vol. 39, núm. 4, p. 513-527.
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