We consider the partitioning of a society i n to coalitions in purely hedonic settings i.e., where each p l a yer's payo is completely determined by the identity of other members of her coalition. We rst discuss how hedonic and non-hedonic settings di er and some su cient conditions for the existence of core stable coalition partitions in hedonic settings. We then focus on a weaker stability condition: individual stability, where no player can bene t from moving to another coalition while not hurting the members of that new coalition. We show that if coalitions can be ordered according to some characteristic over which players have single-peaked preferences, or where players have symmetric and additively separable preferences, then there exists an individually stable coalition partition. Examples show that without these conditions, individually stable coalition partitions may not exist. We also discuss some other stability concepts, and the incompatibility of stability with other normative properties. Keywords: Hedonic Game, Coalition, Individual Stability, Cooperative G a m e JEL Classi cation Numbers: C71, A14, D20. Bogomolnaia is at the Department of Economics, P.O.Box 0496, Southern Methodist University, Dallas, Texas 75275, USA (annab@mail.smu.edu). Jackson is at the division of Humanities and Social Sciences, 228-77, California Institute of Technology, P asadena, California 91125, USA, (jacksonm@hss.caltech.edu). Financial support under NSF grant SBR 9507912 is gratefully acknowledged. We thank Salvador Barbera, Gabrielle Demange, Joseph Greenberg, Michel Le Breton, and Shlomo Weber for very helpful conversations and suggestions. We are also grateful for the comments of two anonymous referees that have helped in the rewriting of the paper.
In another important paper, Bogomolnaia and Jackson REF formalized Nash stability and individual stability in the context of hedonic games and presented a number of sufficient conditions for the existence of various stability concepts.
The Stability of Hedonic Coalition Structures
GAMES AND ECONOMIC BEHAVIOR
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