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In this paper the equal split-off set is introduced as a new solution concept for cooperative games. This solution is based on egalitarian considerations and it turns out that for superadditive games the equal split-off set is a subset of the equal division core. Moreover, the proposed solution is single valued on the class of convex games and it coincides with the Dutta-Ray constrained egalitarian solution.
Top responsiveness was shown by Alcalde and Revilla [AR] to guarantee the existence of core stable partitions in hedonic coalition formation games. In this paper we prove the existence of Nash stable partitions under top responsiveness when a mutuality condition is imposed.
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