Linear efficient and symmetric values for TU-games: Sharing the joint gain of cooperation

Recently, Hermandez-Lamoneda et al. (2008) and independently Chameni and Andjiga (2008) gave an analytic formulation for all valued solutions to the n-person TU-games that satisfy linearity, efficiency and symmetry axioms. Our main purpose in this paper is to recast the proposed formulation to a more potentially interpretational one. We are focused on an interpretation based on the idea of marginal contribution, a concept already familiar in the Shapley value and the Solidarity value. A general null player axiom is introduced, and it turns out that any valued solution satisfying the three properties is characterized by a null player model.