Differential Marginality, Inessential Games and Convex Combinations of Values

The principle of differential marginality (Casajus, 2011) for cooperative games is a very appealing property that requires equal productivity differentials to translate into equal payoff differentials. In this paper we develop several applications of the property in axiomatic characterizations of values. We first show that differential marginality, together with the inessential game property introduced by Ferri`eres (2017) and efficiency, implies additivity and symmetry, and here the inessential game property can be replaced by the nullifying player property or the dummifying player property. Based on these results, we propose new characterizations of the equal division and the equal surplus division values. Finally, we characterize two classes of convex combinations of values, i.e., α-egalitarian Shapley values and α-equal surplus division values, by employing differential marginality and determining the uniqueness of these values on inessential games