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Unique Stability in Simple Coalition Formation Games

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  • Szilvia Papai

    (Universidade Nova de Lisboa)

Abstract

In this paper we study the existence and uniqueness of stable coalition structures, when the value of a coalition to a member depends solely on the other members of the coalition. We search for collections of admissible coalitions that induce uniquely stable coalition structures, that is, ensure that there is a unique stable coalition structure at every preference profile when only admissible coalitions may form. A collection of coalitions satisfies the single-lapping property if (a) no two coalitions have more than one member in common, and (b) in a cycle formed by coalitions with a non-empty intersection all the coalitions have the same member in common. We prove that a collection of coalitions induces a unique stable coalition structure if and only if it satisfies the single-lapping property. We also provide a graph representation of collections of coalitions that satisfy the single-lapping property. This alternative representation is used to explore implications of our characterization result for matching problems such as the marriage and roommate problems. We also discuss the implications for the existence of strategyproof rules of coalition formation.

Suggested Citation

  • Szilvia Papai, 2000. "Unique Stability in Simple Coalition Formation Games," Econometric Society World Congress 2000 Contributed Papers 1537, Econometric Society.
  • Handle: RePEc:ecm:wc2000:1537
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    Cited by:

    1. Demange, Gabrielle, 2009. "The strategy structure of some coalition formation games," Games and Economic Behavior, Elsevier, vol. 65(1), pages 83-104, January.
    2. Carmelo Rodríguez-Álvarez, 2009. "Strategy-proof coalition formation," International Journal of Game Theory, Springer;Game Theory Society, pages 431-452.
    3. Karakaya, Mehmet, 2011. "Hedonic coalition formation games: A new stability notion," Mathematical Social Sciences, Elsevier, vol. 61(3), pages 157-165, May.
    4. Vartiainen, Hannu, 2011. "Dynamic coalitional equilibrium," Journal of Economic Theory, Elsevier, vol. 146(2), pages 672-698, March.
    5. Francis Bloch & Effrosyni Diamantoudi, 2011. "Noncooperative formation of coalitions in hedonic games," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(2), pages 263-280, May.
    6. Vincent Iehlé, 2005. "The core-partition of hedonic games," Cahiers de la Maison des Sciences Economiques b05091, Université Panthéon-Sorbonne (Paris 1).
    7. Robert P. Gilles & Emiliya Lazarova & Pieter H. M. Ruys, 2006. "On Socio-Economic Roles And Specialisation," Economic Papers, The Economic Society of Australia, vol. 25(2), pages 157-170, June.
    8. Hans Gersbach & Hans Haller, 2011. "Bargaining cum voice," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 36(2), pages 199-225, February.
    9. Iehle, Vincent, 2007. "The core-partition of a hedonic game," Mathematical Social Sciences, Elsevier, vol. 54(2), pages 176-185, September.
    10. Hans Gersbach & Hans Haller, 2006. "Voice and Bargaining Power," CESifo Working Paper Series 1668, CESifo Group Munich.
    11. Alison Watts, 2006. "Formation of Segregated and Integrated Groups," Working Papers 2006.127, Fondazione Eni Enrico Mattei.
    12. repec:spr:jogath:v:46:y:2017:i:2:d:10.1007_s00182-016-0538-6 is not listed on IDEAS

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