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Simple Priorities and Core Stability in Hedonic Games

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  • Dinko Dimitrov

    (Center and Department of Econometrics and Operations Research, Tilburg University)

  • Peter Borm

    (Center and Department of Econometrics and Operations Research, Tilburg University)

  • Ruud Hendrickx

    (Center and Department of Econometrics and Operations Research, Tilburg University)

  • Shao Chin Sung

    (School of Information Science, Japan Advanced Institute of Science and Technology)

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.

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Bibliographic Info

Paper provided by Fondazione Eni Enrico Mattei in its series Working Papers with number 2004.51.

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Date of creation: Mar 2004
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Handle: RePEc:fem:femwpa:2004.51

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Keywords: Additive separability; Coalition formation; Core stability; Hedonic games; NP-completeness; Priority;

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References

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  1. Alcalde, Jose & Revilla, Pablo, 2004. "Researching with whom? Stability and manipulation," Journal of Mathematical Economics, Elsevier, vol. 40(8), pages 869-887, December.
  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. Ballester, Coralio, 2004. "NP-completeness in hedonic games," Games and Economic Behavior, Elsevier, vol. 49(1), pages 1-30, October.
  4. Antonio Romero-Medina & Katari´na Cechlárová, 2001. "Stability in coalition formation games," International Journal of Game Theory, Springer, vol. 29(4), pages 487-494.
  5. Bogomolnaia, Anna & Jackson, Matthew O., 2002. "The Stability of Hedonic Coalition Structures," Games and Economic Behavior, Elsevier, vol. 38(2), pages 201-230, February.
  6. Burani, Nadia & Zwicker, William S., 2003. "Coalition formation games with separable preferences," Mathematical Social Sciences, Elsevier, vol. 45(1), pages 27-52, February.
  7. 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.
  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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Citations

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Cited by:
  1. 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.
  2. Shao Chin Sung & Dinko Dimitrov, 2005. "A taxonomy of myopic stability concepts for hedonic games," Working Papers 373, Bielefeld University, Center for Mathematical Economics.
  3. Karakaya, Mehmet, 2011. "Hedonic coalition formation games: A new stability notion," Mathematical Social Sciences, Elsevier, vol. 61(3), pages 157-165, May.
  4. Carmelo Rodriguez-Alvarez, 2005. "Strategy-Proof Coalition Formation," Economics Working Papers we055525, Universidad Carlos III, Departamento de Economía.
  5. 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.
  6. Vincent Iehlé, 2005. "The core-partition of hedonic games," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00197528, HAL.
  7. 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.
  8. Alison Watts, 2007. "Formation of segregated and integrated groups," International Journal of Game Theory, Springer, vol. 35(4), pages 505-519, April.
  9. Arlegi, Ritxar & Dimitrov, Dinko, 2008. "Dichotomous Preferences and Power Set Extensions," Discussion Papers in Economics 6431, University of Munich, Department of Economics.
  10. Dinko Dimitrov & Shao Chin Sung, 2011. "Size Monotonicity and Stability of the Core in Hedonic Games," Working Papers 2011.52, Fondazione Eni Enrico Mattei.
  11. Iehle, Vincent, 2007. "The core-partition of a hedonic game," Mathematical Social Sciences, Elsevier, vol. 54(2), pages 176-185, September.
  12. Shao Sung & Dinko Dimitrov, 2007. "On Myopic Stability Concepts for Hedonic Games," Theory and Decision, Springer, vol. 62(1), pages 31-45, February.
  13. Alison Watts, 2006. "Formation of Segregated and Integrated Groups," Working Papers 2006.127, Fondazione Eni Enrico Mattei.

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