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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.

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Bibliographic Info

Paper provided by Econometric Society in its series Econometric Society World Congress 2000 Contributed Papers with number 1537.

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Date of creation: 01 Aug 2000
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Handle: RePEc:ecm:wc2000:1537

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  1. Chung, Kim-Sau, 2000. "On the Existence of Stable Roommate Matchings," Games and Economic Behavior, Elsevier, vol. 33(2), pages 206-230, November.
  2. Tayfun Sönmez & Suryapratim Banerjee & Hideo Konishi, 2001. "Core in a simple coalition formation game," Social Choice and Welfare, Springer, vol. 18(1), pages 135-153.
  3. Ma, Jinpeng, 1994. "Strategy-Proofness and the Strict Core in a Market with Indivisibilities," International Journal of Game Theory, Springer, vol. 23(1), pages 75-83.
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  8. Alkan, Ahmet, 1988. "Nonexistence of stable threesome matchings," Mathematical Social Sciences, Elsevier, vol. 16(2), pages 207-209, October.
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  13. Barbera, Salvador & Gerber, Anke, 2003. "Corrigendum to "On coalition formation: durable coalition structures": [Mathematical Social Sciences 45 (2003) 185-203]," Mathematical Social Sciences, Elsevier, vol. 46(3), pages 355-356, December.
  14. Roth, Alvin E., 1982. "Incentive compatibility in a market with indivisible goods," Economics Letters, Elsevier, vol. 9(2), pages 127-132.
  15. Burani, Nadia & Zwicker, William S., 2003. "Coalition formation games with separable preferences," Mathematical Social Sciences, Elsevier, vol. 45(1), pages 27-52, February.
  16. José Alcalde & Pablo Revilla, 2003. "Researching with Whom? Stability and Manipulation," Economic Working Papers at Centro de Estudios Andaluces E2003/35, Centro de Estudios Andaluces.
  17. Bogomolnaia, Anna & Jackson, Matthew O., 2002. "The Stability of Hedonic Coalition Structures," Games and Economic Behavior, Elsevier, vol. 38(2), pages 201-230, February.
  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. Ehud Kalai, 1978. "A Group Incentive Compatible Mechanism Yielding Core Allocation," Discussion Papers 329, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  20. Roth, Alvin E. & Postlewaite, Andrew, 1977. "Weak versus strong domination in a market with indivisible goods," Journal of Mathematical Economics, Elsevier, vol. 4(2), pages 131-137, August.
  21. José Alcalde & Antonio Romero Medina, 2005. "Coaliton Formation And Stability," Working Papers. Serie AD 2005-21, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  22. Sotomayor, Marilda, 1996. "A Non-constructive Elementary Proof of the Existence of Stable Marriages," Games and Economic Behavior, Elsevier, vol. 13(1), pages 135-137, March.
  23. Greenberg, Joseph & Weber, Shlomo, 1986. "Strong tiebout equilibrium under restricted preferences domain," Journal of Economic Theory, Elsevier, vol. 38(1), pages 101-117, February.
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Citations

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Cited by:
  1. Vartiainen, Hannu, 2011. "Dynamic coalitional equilibrium," Journal of Economic Theory, Elsevier, vol. 146(2), pages 672-698, March.
  2. Gilles, R.P. & Lazarova, E.A. & Ruys, P.H.M., 2006. "Stability, Specialization and Social Recognition," Discussion Paper 2006-17, Tilburg University, Center for Economic Research.
  3. Carmelo Rodríguez Álvarez, 2006. "Strategy-Proof Coalition Formation," Economic Working Papers at Centro de Estudios Andaluces E2006/11, Centro de Estudios Andaluces.
  4. Hans Gersbach & Hans Haller, 2006. "Voice and Bargaining Power," CESifo Working Paper Series 1668, CESifo Group Munich.
  5. 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.
  6. Vincent Iehlé, 2005. "The core-partition of hedonic games," Cahiers de la Maison des Sciences Economiques b05091, Université Panthéon-Sorbonne (Paris 1).
  7. Gersbach, Hans & Haller, Hans, 2010. "Bargaining cum Voice," CEPR Discussion Papers 7774, C.E.P.R. Discussion Papers.
  8. 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.
  9. repec:hal:wpaper:halshs-00590290 is not listed on IDEAS
  10. Karakaya, Mehmet, 2011. "Hedonic coalition formation games: A new stability notion," Mathematical Social Sciences, Elsevier, vol. 61(3), pages 157-165, May.
  11. Gabrielle Demange, 2006. "The strategy structure of some coalition formation games," PSE Working Papers halshs-00590290, HAL.
  12. Iehle, Vincent, 2007. "The core-partition of a hedonic game," Mathematical Social Sciences, Elsevier, vol. 54(2), pages 176-185, September.
  13. 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.
  14. 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.
  15. 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.
  16. Alison Watts, 2006. "Formation of Segregated and Integrated Groups," Working Papers 2006.127, Fondazione Eni Enrico Mattei.

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