On the asymmetric Shapley value for cooperative games (Q1396732)

The referred paper contributes to the theory of cooperative games with finite set of players and defined in the characteristic function form. All attention is focused on the properties of the Shapley value, its generalization called asymmetric Shapley value, and their relation. The asymmetry consists in the existence of weights modifying the combinatorical coefficients in the Shapley formula. The main results specify the influence of the choice of the weights and the combinatorical coefficient of the grand coalition of all players on the probabilistic character of the set of coefficients including the monotonicity and Schur-concavity of certain combination of coefficients.