André Casajus, Pierfrancesco La Mura

• We suggest a new component efficient solution for monotonic TU games with a coalition structure, the conditional Shapley value. Other than other such solutions, it satisfies the null player property. Nevertheless, it accounts for the players‘ outside options in productive components of coalition structures. For all monotonic games, there exist coalition structures that are stable under the conditional Shapley value. For voting games, the stability of coalition structures under the conditional Shapley value supports Gamson‘s theory of coalition formation (Gamson, Am Sociol Rev 26, 1961, 373-382).