One More Uniqueness of the Shapley Value

The class of TU games whose maximal per capita characteristic function values are attained on the grand coalition. Three axiomatic characterizations of the Shapley value — Shapley’s original axiomatization, Sobolev’s axiomatization with the aid of consistency, and Young’s axiomatization by means of marginality — are used for the corresponding axiomatization of the Shapley value on the class of totally cooperative games. It is shown that only two last axiomatizations characterize the Shapley value uniquely, and Shapley’s axiomatization leads to linear combinations of the Shapley value and the egalitarian value.