Individual Preference Restrictions in Hedonic Coalition Formation Games∗

In this paper we study restrictions imposed on individual preferences, as opposed to preference profiles, and we introduce individual preference restrictions that characterize the existence and uniqueness of stable hedonic coalition structures on rich preference domains. We prove that if such a preference domain satisfies an individual preference restriction then it guarantees the existence of a stable coalition structure if and only if it satisfies Intersection Restriction. Intersection Restriction requires that the intersection of any two strongly individually rational coalitions is ranked weakly above at least one of them. We also present a similar characterization result for the uniqueness of a stable coalition structure by the individual preference restrictions of Superset Restriction and Strong Intersection Restriction. Superset Restriction is satisfied if a strongly individually rational coalition that is ranked above another one is always a superset of the latter, while Strong Intersection Restriction requires that the intersection of any two strongly individually rational coalitions is ranked weakly above both coalitions.