Null players, solidarity, and the egalitarian Shapley values

The Shapley value certainly is the most eminent single-point solution concept for TU-games. In its standard characterization, the null player property indicates the absence of solidarity among the players. First, we replace the null player property by a new axiom that guarantees null players non-negative payoffs whenever the grand coalition's worth is non-negative. Second, the equal treatment property is strengthened into desirability. This way, we obtain a new characterization of the class of egalitarian Shapley values, i.e., of convex combinations of the Shapley value and the equal division solution. We complement this result by characterizations of the class of generalized consensus values, i.e., of convex combinations of the Shapley value and the equal surplus division solution.