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Simple Priorities and Core Stability in Hedonic Games

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  • Dimitrov, D.A.
  • Borm, P.E.M.
  • Hendrickx, R.L.P.
  • Sung, S.C.

    (Tilburg University, Center for Economic Research)

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 su.cient conditions for non-emptiness of the core already known in the literature.

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Bibliographic Info

Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 2004-5.

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Date of creation: 2004
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Handle: RePEc:dgr:kubcen:20045

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Web page: http://center.uvt.nl

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Keywords: core; stability; games;

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References

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  1. Antonio Romero-Medina & Katari´na Cechlárová, 2001. "Stability in coalition formation games," International Journal of Game Theory, Springer, vol. 29(4), pages 487-494.
  2. Herbert E. Scarf, 1965. "The Core of an N Person Game," Cowles Foundation Discussion Papers 182R, Cowles Foundation for Research in Economics, Yale University.
  3. 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.
  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. Burani, Nadia & Zwicker, William S., 2003. "Coalition formation games with separable preferences," Mathematical Social Sciences, Elsevier, vol. 45(1), pages 27-52, February.
  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. Dreze, J H & Greenberg, J, 1980. "Hedonic Coalitions: Optimality and Stability," Econometrica, Econometric Society, vol. 48(4), pages 987-1003, May.
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Cited by:
  1. Iehle, Vincent, 2007. "The core-partition of a hedonic game," Mathematical Social Sciences, Elsevier, vol. 54(2), pages 176-185, September.
  2. Alison Watts, 2006. "Formation of Segregated and Integrated Groups," Working Papers 2006.127, Fondazione Eni Enrico Mattei.
  3. Iehlé, Vincent, 2007. "The Core-Partition of Hedonic Games," Economics Papers from University Paris Dauphine 123456789/87, Paris Dauphine University.
  4. Shao Chin Sung & Dinko Dimitrov, 2005. "A taxonomy of myopic stability concepts for hedonic games," Working Papers 373, Bielefeld University, Center for Mathematical Economics.
  5. Sung, Shao-Chin & Dimitrov, Dinko, 2008. "Computational Complexity in Additive Hedonic Games," Discussion Papers in Economics 6430, University of Munich, Department of Economics.
  6. Carmelo Rodríguez-Álvarez, 2009. "Strategy-proof coalition formation," International Journal of Game Theory, Springer, vol. 38(3), pages 431-452, November.
  7. repec:lmu:muenec:6431 is not listed on IDEAS
  8. Woeginger, Gerhard J., 2013. "A hardness result for core stability in additive hedonic games," Mathematical Social Sciences, Elsevier, vol. 65(2), pages 101-104.
  9. Shao Sung & Dinko Dimitrov, 2007. "On Myopic Stability Concepts for Hedonic Games," Theory and Decision, Springer, vol. 62(1), pages 31-45, February.
  10. 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.
  11. Alison Watts, 2007. "Formation of segregated and integrated groups," International Journal of Game Theory, Springer, vol. 35(4), pages 505-519, April.
  12. 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.
  13. Karakaya, Mehmet, 2011. "Hedonic coalition formation games: A new stability notion," Mathematical Social Sciences, Elsevier, vol. 61(3), pages 157-165, May.
  14. Dinko Dimitrov & Shao Chin Sung, 2011. "Size Monotonicity and Stability of the Core in Hedonic Games," Working Papers 2011.52, Fondazione Eni Enrico Mattei.
  15. Kleinberg, Jon & Ligett, Katrina, 2013. "Information-sharing in social networks," Games and Economic Behavior, Elsevier, vol. 82(C), pages 702-716.

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