Individual Stability in Hedonic Coalition Formation

I 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 to which they belong. 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 feasible coalitions, which are assumed to include all singletons. In this paper I give characterizations, in terms of restrictions on feasible 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 cannot be feasible, while for individual stability odd single-lapping cycles, together with certain disjoint subsets of the coalitions in the cycle, are not feasible. Based on these characterizations, sufficient conditions for the Nash-stability and individual stability of preference profiles are also provided. ∗I would like to thank Rajat Deb, Gabrielle Demange, Federico Echenique, and Lars Ehlers for their comments, as well as the participants of the 2006 Wallis Institute Mini Conference. †Department of Economics, Concordia University, 1455 de Maisonneuve Blvd. West, Montreal, Quebec H3G 1M8, Canada; e-mail: [email protected]