Nash bargaining, Shapley threats, and outside options

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 asymmetric treatment of outside options. Further, the stability of coalition structures is explored. These concepts are applied to apex games.