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Equity properties of the Shapley value as a power index

Malawski M.

Control and Cybernetics

2002

Vol. 31, no 1

117-127

We study power indices for simple games which have the following "uniform transfer property" : when only one losing coalition in a game becomes winning, worths of all other coalitions remaining unchanged, the index increases equally for all players in that coalition and decreases equally for all players not in that coalition. We show that both for superadditive simple games and for all simple games there is only one such index : the Shapley-Shubik index, the restriction of Shapley value to the class of simple games. Moreover, the proof of this fact does not even require the standard assumption of symmetry of power indices which can be replaced by a weaker equal treatment condition.