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Simple Priorities and Core Stability in Hedonic Games

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Author Info

  • Dinko Dimitrov

    ()

  • Peter Borm

    ()

  • Ruud Hendrickx

    ()

  • Shao Sung

    ()

Abstract

In this paper we study hedonic games where each player views every other player either as a friend or as an enemy. Two simple priority criteria for comparison of coalitions are suggested, and the corresponding preference restrictions based on appreciation of friends and aversion to enemies are considered. It turns out that the first domain restriction guarantees non-emptiness of the strong core and the second domain restriction ensures non-emptiness of the weak core of the corresponding hedonic games. Moreover, an element of the strong core under friends appreciation can be found in polynomial time, while finding an element of the weak core under enemies aversion is NP-hard. We examine also the relationship between our domain restrictions and some sufficient conditions for non-emptiness of the core already known in the literature.

(This abstract was borrowed from another version of this item.)

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Bibliographic Info

Article provided by Springer in its journal Social Choice and Welfare.

Volume (Year): 26 (2006)
Issue (Month): 2 (April)
Pages: 421-433

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Handle: RePEc:spr:sochwe:v:26:y:2006:i:2:p:421-433

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References

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  1. Dreze, J H & Greenberg, J, 1980. "Hedonic Coalitions: Optimality and Stability," Econometrica, Econometric Society, vol. 48(4), pages 987-1003, May.
  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. Burani, Nadia & Zwicker, William S., 2003. "Coalition formation games with separable preferences," Mathematical Social Sciences, Elsevier, vol. 45(1), pages 27-52, February.
  4. Alcalde, Jose & Revilla, Pablo, 2004. "Researching with whom? Stability and manipulation," Journal of Mathematical Economics, Elsevier, vol. 40(8), pages 869-887, December.
  5. Antonio Romero-Medina & Katari´na Cechlárová, 2001. "Stability in coalition formation games," International Journal of Game Theory, Springer, vol. 29(4), pages 487-494.
  6. Ballester, Coralio, 2004. "NP-completeness in hedonic games," Games and Economic Behavior, Elsevier, vol. 49(1), pages 1-30, October.
  7. Bogomolnaia, Anna & Jackson, Matthew O., 2002. "The Stability of Hedonic Coalition Structures," Games and Economic Behavior, Elsevier, vol. 38(2), pages 201-230, February.
  8. Herbert E. Scarf, 1965. "The Core of an N Person Game," Cowles Foundation Discussion Papers 182R, Cowles Foundation for Research in Economics, Yale University.
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Citations

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Cited by:
  1. Sung, Shao-Chin & Dimitrov, Dinko, 2010. "Computational complexity in additive hedonic games," European Journal of Operational Research, Elsevier, vol. 203(3), pages 635-639, June.
  2. repec:hal:cesptp:halshs-00197528 is not listed on IDEAS
  3. Kleinberg, Jon & Ligett, Katrina, 2013. "Information-sharing in social networks," Games and Economic Behavior, Elsevier, vol. 82(C), pages 702-716.
  4. Karakaya, Mehmet, 2011. "Hedonic coalition formation games: A new stability notion," Mathematical Social Sciences, Elsevier, vol. 61(3), pages 157-165, May.
  5. Shao Sung & Dinko Dimitrov, 2007. "On Myopic Stability Concepts for Hedonic Games," Theory and Decision, Springer, vol. 62(1), pages 31-45, February.
  6. Carmelo Rodríguez Álvarez, 2006. "Strategy-Proof Coalition Formation," Economic Working Papers at Centro de Estudios Andaluces E2006/11, Centro de Estudios Andaluces.
  7. Iehle, Vincent, 2007. "The core-partition of a hedonic game," Mathematical Social Sciences, Elsevier, vol. 54(2), pages 176-185, September.
  8. Vincent Iehlé, 2005. "The core-partition of hedonic games," Cahiers de la Maison des Sciences Economiques b05091, Université Panthéon-Sorbonne (Paris 1).
  9. Alison Watts, 2006. "Formation of Segregated and Integrated Groups," Working Papers 2006.127, Fondazione Eni Enrico Mattei.
  10. Dinko Dimitrov & Shao Chin Sung, 2006. "A Taxonomy of Myopic Stability Concepts for Hedonic Games," Working Papers 2006.10, Fondazione Eni Enrico Mattei.
  11. José Alcantud & Ritxar Arlegi, 2012. "An axiomatic analysis of ranking sets under simple categorization," SERIEs, Spanish Economic Association, vol. 3(1), pages 227-245, March.
  12. Dinko Dimitrov & Shao Chin Sung, 2011. "Size Monotonicity and Stability of the Core in Hedonic Games," Working Papers 2011.52, Fondazione Eni Enrico Mattei.
  13. Dimitrov, D.A. & Sung, S.C., 2004. "Enemies and Friends in Hedonic Games: Individual Deviations, Stability and Manipulation," Discussion Paper 2004-111, Tilburg University, Center for Economic Research.
  14. Alison Watts, 2007. "Formation of segregated and integrated groups," International Journal of Game Theory, Springer, vol. 35(4), pages 505-519, April.
  15. repec:lmu:muenec:6431 is not listed on IDEAS
  16. Woeginger, Gerhard J., 2013. "A hardness result for core stability in additive hedonic games," Mathematical Social Sciences, Elsevier, vol. 65(2), pages 101-104.

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