We provide a new characterization of the Shapley value neither using the efficiency axiom nor the additivity axiom. In this characterization, efficiency is replaced by the gain-loss axiom (Einy and Haimanko, 2011), i.e., whenever the total worth generated does not change, a player can only gain...

We introduce a weighted version of the component efficient χ-value [Casajus, A., 2009. Outside options, component efficiency, and stability. Games and Economic Behavior 65 (1), 49–61] for TU games with a coalition structure. We provide characterizations both for a symmetric and for an...