| Abstract: | The Semivalues were introduced by Dubey, Neiman and Weber (1981), as the values of TU games satisfying a set of axioms, precisely:linearity, symmetry, monotomcity and projection axioms. In this paper, a potential approach is used to prove a characterization of Semivalues as the unique values satisfying a new type of consistency relative to a new implicitly defined reduced game of Hart Mas Colell type and weighted standardness for all two person games. The definition of the reduced game requires some combinatorial results on the auxiliary game of the given game. As a byproduct, we derive from these results two other combinatorial properties of the Semivalues: (i) any Semivalue is the Shapley value of the auxiliary game of the given game, and (ii) any Semivalue satisfies the fairness principle introduced by Myerson (1977) as the principle of balanced contributions |
