ON AXIOMATIZATIONS OF THE WEIGHTED SHAPLEY VALUES

The family of weighted Shapley values for cooperative n-person transfe rable utility games is studied. We assume first that the weights of th e players are given exogenously and provide two axiomatic characteriza tions of the corresponding weighted Shapley value. Our first character ization is based on the classical axioms determining the Shapley value with the symmetry axiom replaced by a new postulate called the omega- mutual dependence. In our second axiomatization we use among other thi ngs the strong monotonicity property of Young (1985, Int. J. Game Theo ry 14, 65-72). Finally, we give a new axiomatic characterization of th e family of all weighted Shapley values. (C) 1995 Academic Press, Inc.