New characterizations of the Shapley value using weak differential marginalities

Abstract

The principle of differential marginality for cooperative games states that the payoff differential of two players does not change whenever their productivity differential, measured by the differentials of their marginal contributions to coalitions containing neither of them, does not change. The hypothesis of differential marginality is satisfied if and only if the two players are symmetric in the difference of the two games under consideration. In this paper we introduce two weakened variants of differential marginality in which symmetric players in the difference of the two games are replaced by mutually dependent players and necessary players, respectively. By combining these weakened versions of differential marginality with the standard axioms: efficiency and either the null player out property or the disjointly productive players property, we provide two new characterizations of the Shapley value for the setting of variable player sets.