Anonymous and Separable Hedonic Coalition Formation Games: Nash Stability Under Different Membership Rights
Journal: Business and Economics Research Journal (BERJ) (Vol.14, No. 3)Publication Date: 2023-07-28
Authors : Mehmet Karakaya Seçkin Özbilen;
Page : 303-319
Keywords : Coalition Formation; Hedonic Games; Nash Stability; Membership Rights;
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.
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