Individual Stability in Hedonic Coalition Formation




We study the existence of Nash stable and individually stable coalition structures in hedonic coalition formation games, where a coalition structure is a partition of the players, and players strictly rank the coalitions that they belong to. The hedonic coalition formation game in which all coalitions are feasible is viewed as a general model, and more specific models, such as the marriage and roommate models, are defined by the set of admissible coalitions, which are assumed to include all singletons. In this paper we give characterizations, in terms of restrictions on admissible coalitions, of the hedonic coalition formation models which are Nash stable and individually stable, respectively, in the sense that at least one such coalition structure exists for all preference profiles in the given model. In particular, the result for Nash stability is that coalitions of size two are inadmissible, while for individual stability single-lapping odd cycles, together with certain specified disjoint subsets of the coalitions in the odd cycle, are inadmissible.