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Unique stability in simple coalition formation games

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  • Papai, Szilvia

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.

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Bibliographic Info

Article provided by Elsevier in its journal Games and Economic Behavior.

Volume (Year): 48 (2004)
Issue (Month): 2 (August)
Pages: 337-354

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Handle: RePEc:eee:gamebe:v:48:y:2004:i:2:p:337-354

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Web page: http://www.elsevier.com/locate/inca/622836

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  1. Alkan, Ahmet, 1988. "Nonexistence of stable threesome matchings," Mathematical Social Sciences, Elsevier, vol. 16(2), pages 207-209, October.
  2. Tayfun Sonmez, 1999. "Strategy-Proofness and Essentially Single-Valued Cores," Econometrica, Econometric Society, vol. 67(3), pages 677-690, May.
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  5. José Alcalde, 1995. "Exchange-Proofness or Divorce-Proofness? Stability in One-Sided Matching Markets," Working Papers. Serie AD 1995-04, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
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  14. Antonio Romero-Medina & Katari´na Cechlárová, 2001. "Stability in coalition formation games," International Journal of Game Theory, Springer, vol. 29(4), pages 487-494.
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  18. Alcalde, J. & Barberà, S., 1992. "Top Dominance and the Possibility of Strategy-Proof Stable Solutions to Matching Problems," UFAE and IAE Working Papers 196.92, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  19. Burani, Nadia & Zwicker, William S., 2003. "Coalition formation games with separable preferences," Mathematical Social Sciences, Elsevier, vol. 45(1), pages 27-52, February.
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Citations

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Cited by:
  1. Robert P. Gilles & Emiliya A. Lazarova & Pieter H. M. Ruys, 2007. "Stability, Specialization And Social Recognition," Division of Labor & Transaction Costs (DLTC), World Scientific Publishing Co. Pte. Ltd., vol. 2(02), pages 83-109.
  2. Hans Gersbach & Hans Haller, 2006. "Voice and Bargaining Power," CESifo Working Paper Series 1668, CESifo Group Munich.
  3. Demange, Gabrielle, 2009. "The strategy structure of some coalition formation games," Games and Economic Behavior, Elsevier, vol. 65(1), pages 83-104, January.
  4. repec:hal:cesptp:halshs-00197528 is not listed on IDEAS
  5. Carmelo Rodriguez-Alvarez, 2005. "Strategy-Proof Coalition Formation," Economics Working Papers we055525, Universidad Carlos III, Departamento de Economía.
  6. Vartiainen, Hannu, 2011. "Dynamic coalitional equilibrium," Journal of Economic Theory, Elsevier, vol. 146(2), pages 672-698, March.
  7. Iehlé, Vincent, 2007. "The Core-Partition of Hedonic Games," Economics Papers from University Paris Dauphine 123456789/87, Paris Dauphine University.
  8. Francis Bloch & Effrosyni Diamantoudi, 2011. "Noncooperative formation of coalitions in hedonic games," International Journal of Game Theory, Springer, vol. 40(2), pages 263-280, May.
  9. Gilles, R.P. & Lazarova, E.A. & Ruys, P.H.M., 2011. "Economic Institutions and Stability: A Network Approach," Discussion Paper 2011-084, Tilburg University, Center for Economic Research.
  10. 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, 06.
  11. Noemí Navarro, 2008. "A Sensitive Flexible Network Approach," Working Papers 2008-2, Universidad de Málaga, Department of Economic Theory, Málaga Economic Theory Research Center, revised Sep 2008.
  12. Hans Gersbach & Hans Haller, 2011. "Bargaining cum voice," Social Choice and Welfare, Springer, vol. 36(2), pages 199-225, February.
  13. Alison Watts, 2006. "Formation of Segregated and Integrated Groups," Working Papers 2006.127, Fondazione Eni Enrico Mattei.
  14. Robert P. Gilles & Emiliya Lazarova & Pieter H.M. Ruys, 2006. "On Socio-economic Roles and Specialization," Tinbergen Institute Discussion Papers 06-035/2, Tinbergen Institute.
  15. Gabrielle Demange, 2006. "The strategy structure of some coalition formation games," Working Papers halshs-00590290, HAL.

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