Cohesive efficiency in TU-games: axiomatizations of variants of the Shapley value, egalitarian values and their convex combinations

We relax the assumption that the grand coalition must form by imposing the axiom of Cohesive efficiency: the total payoffs that the players can share is equal to the maximal total worth generated by a coalition structure. We determine how the three main axiomatic characterizations of the Shapley value are affected when the classical axiom of Efficiency is replaced by Cohesive efficiency. We introduce and characterize two variants of the Shapley value that are compatible with Cohesive efficiency. We show that our approach can also be applied to the variants of more egalitarian values.