Cataloged from PDF version of article.This paper studies hedonic coalition formation games where each player's preferences rely only upon the members of her coalition. A new stability notion under free exit-free entry membership rights, referred to as strong Nash stability, is introduced which is stronger than both core and Nash stabilities studied earlier in the literature. Strong Nash stability has an analogue in non-cooperative games and it is the strongest stability notion appropriate to the context of hedonic coalition formation games. The weak top-choice property is introduced and shown to be sufficient for the existence of a strongly Nash stable partition. It is also shown that descending separable preferences guarantee the existence of a strongly Nash stable partition. Strong Nash stability under different membership rights is also studied. (C) 2011 Elsevier B.V. All rights reserved

We consider hedonic coalition formation games with variable sets of agents and extend the properties competition sensitivity and resource sensitivity (introduced by Klaus, 2011, for roomate markets) to hedonic coalition formation games. Then, we show that on the domain of solvable hedonic coalition formation games, the Core is characterized by coalitional unanimity and Maskin monotonicity (see also Takamiya, 2010, Theorem 1). Next, we characterize the Core for solvable hedonic coalition formation games by unanimity, Maskin monotonicity, and either competition sensitivity or resource sensitivity (Corollary 2). Finally, and in contrast to roommate markets, we show that on the domain of solvable hedonic coalition formation games, there exists a solution not equal to the Core that satisfies coalitional unanimity, consistency, competition sensitivity, and resource sensitivity (Example 2).

We study the house allocation with existing tenants model (introduced by Abdulkadiroglu and Sönmez, 1999) and consider rules that allocate houses based on priorities. We introduce a new acyclicity requirement for the underlying priority structure which is based on the acyclicity conditions by Ergin (2002) and Kesten (2006) for house allocation with quotas and without existing tenants. We show that for house allocation with existing tenants a top trading cycles rules is consistent if and only if its underlying priority structure satisfies our acyclicity condition. Moreover, even if no priority structure is a priori given, we show that a rule is a top trading cycles rule based on ownership-adapted acyclic priorities if and only if it satisfies Pareto-optimality, individual-rationality, strategy-proofness, reallocation-proofness, and consistency.

Purpose - We study hedonic coalition formation games in which each agent has preferences over the coalitions she is a member of. Hedonic coalition formation games are used to model economic, social, and political instances in which people form coalitions. The outcome of a hedonic coalition formation game is a partition. We consider stability concepts of a partition that are based on a single-agent deviation under different membership rights, that is, we study Nash stability under different membership rights. We revisit the conditions that guarantee the existence of Nash stable partitions and provide examples of hedonic coalition formation games satisfying these conditions. Methodology – While analyzing a stability notion for hedonic coalition formation games, two crucial points are considered: i) who can deviate from the given partition, ii) what are the allowed movements for the deviator(s), i.e., what deviators are entitled to do. For the first point, the deviation of a single agent is considered for Nash stabilities. For the second point, the allowed movements for deviators are determined by specifying membership rights, that is, membership rights describe whose approval is needed for a particular deviation. So, we reconsider stability concepts by using membership rights based on individual deviations, i.e., we consider Nash stability under different membership rights for hedonic coalition formation games. Findings- A classification of stability concepts based on a single-agent deviation for hedonic coalition formation games are provided by employing membership rights. The conditions in the literature guaranteeing the existence of Nash stable partitions for all membership rights are revisited. For each condition, an example of a hedonic coalition formation game satisfying the condition is given. Hence, a complete analysis of sufficient conditions for all Nash stability concepts are provided. Conclusion- To choose the correct stability notion one first should understand the membership rights in the environment that she studies. Then, for hedonic coalition formation problems, the appropriate Nash stability notion consistent with the ongoing membership rights should be chosen when single-agent deviation is considered. Keywords: Coalition formation, Hedonic games, Nash stability, membership rights, separable preferences JEL Codes: C71, C78, D71

We study hedonic coalition formation games that consist of a finite set of agents and a list of agents’ preferences such that each agent’s preferences depend only on the members of her coalition. An outcome of a hedonic coalition formation game is a partition (i.e., coalition structure) of the finite set of agents. We study the existence of partitions that are both internally stable and Pareto optimal. We construct an algorithm that terminates for each given hedonic coalition formation game such that the outcome of the algorithm is internally stable and Pareto optimal. We also show that if the outcome of the algorithm is the partition that consists of singleton coalitions then it is also core stable and if it is the partition that contains only the grand coalition then it is also both core stable and Nash stable.