Working Papers / Work in Progress


Abstract: We study hedonic coalition formation problems with friend-oriented preferences; that is, each agent has preferences over his coalitions based on a partition of the set of agents, except himself, into friends and enemies such that (E) adding an enemy makes him strictly worse o and (F) adding a friend together with a set of enemies makes him strictly better off. Friend-oriented preferences induce a so-called friendship graph where vertices are agents and directed edges point to friends. We show that the partition associated with the strongly connected components (SCC) of the friendship graph is in the strict core. We then prove that the SCC mechanism, which assigns the SCC partition to each hedonic coalition formation problem with friend-oriented preferences, satisfies a strong group incentive compatibility property: group strategyproofness. Our main result is that on any rich subdomain of friend-oriented preferences, the SCC mechanism is the only mechanism that satises core stability and strategyproofness.


Abstract: We study hedonic coalition formation problems in which each agent’s preference depends only on the members of her coalition. We analyze a new stability concept called core-exchange stability that is stronger than both core stability and exchange stability. We discuss the existence of core-exchange stable outcomes in various domains of preferences. We show that some of the domains that guarantee the existence of a core stable outcome are not sufficient for the existence of a non-trivial core-exchange stable outcome. Then, we prove that the domains of preferences satisfying the weak top coalition property of Banerjee et al. (2001), the top responsiveness property of Alcalde and Revilla (2004), and the bottom responsiveness property of Suzuki and Sung (2010) always guarantee the existence of core-exchange stable outcomes.


Abstract: We study the refined bargaining set (Zhou, 1994) and the consistent bargaining set (Dutta et al., 1989) for hedonic games in order to rehabilitate the deficit of ignoring the justifiability and consistency of coalition structures. The key idea of the bargaining set is to distinguish coalition structures that are justifiable from unjustified ones. The consistent bargaining set distinguishes consistent coalition structures, as well as justifiable ones. A coalition structure is called justifiable if and only if it is impossible to invalidate it via some coalitional breaking of agreements. If it is impossible to break an agreement via successive coalitional recants, then a coalition structure is called consistent. This research project consists of two main parts. In the first part, we study the non-emptiness of the bargaining set and the consistent bargaining set. We analyze the non-emptiness of the bargaining set in the domain of all hedonic games. Moreover, we investigate in which domains, the bargaining set and the consistent bargaining set, the core, and the consistent bargaining set, or all together coincide with each other. The second part of this project is constructed upon the first part. We analyze the characterization of coalition formation rules which assign coalition structures in the bargaining set and in the consistent bargaining set.

Publications


Business and Economics Research Journal, 2023, 14(3): 303 - 319.

Abstract: We consider hedonic coalition formation games. A hedonic coalition formation game is a pair which consists of a finite set of agents and a list of agents’ preferences such that each agent has preferences over all coalitions containing her. We study the existence of a Nash stable partition under different membership rights for anonymous and separable hedonic coalition formation games. We prove that for anonymous and separable hedonic games, the existence of a Nash stable partition is always guaranteed when the membership rights are Free Exit-Approved Entry or Approved Exit-Free Entry, but the existence of a Nash stable partition is not guaranteed when the membership rights are Free Exit-Free Entry. We also analyze the relation of the anonymity and separability with the other sufficient conditions which guarantee the existence of a Nash stable partition under different membership rights.


Journal of Business, Economics, and Finance, 2023, 12(1): 45 - 58.

Abstract: 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.


Journal of Management and Economics Research, 2022, 20(4): 335 - 350.

Abstract: 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.


Ankara University SBF Journal, 2022, 77(4): 853 - 875.

Abstract: This paper is on hedonic coalition formation games. We focus on a new stability concept called internal stability and introduce an algorithm that always brings internally stable coalition structures. Firstly, we analyze the relation between internal stability and other stability concepts. Then, we prove that the algorithm we introduce also brings non-trivial internally stable coalition structures in the full domain. Then, we analyze the relation between trivial coalition structures and the behavior of the algorithm.