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Simple Priorities and Core Stability in Hedonic Games

Author

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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.

Suggested Citation

  • Dinko Dimitrov & Peter Borm & Ruud Hendrickx & Shao Chin Sung, 2004. "Simple Priorities and Core Stability in Hedonic Games," Working Papers 2004.51, Fondazione Eni Enrico Mattei.
  • Handle: RePEc:fem:femwpa:2004.51
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    References listed on IDEAS

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    1. Dinko Dimitrov & Peter Borm & Ruud Hendrickx & Shao Sung, 2006. "Simple Priorities and Core Stability in Hedonic Games," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 26(2), pages 421-433, April.
    2. Alcalde, Jose & Revilla, Pablo, 2004. "Researching with whom? Stability and manipulation," Journal of Mathematical Economics, Elsevier, vol. 40(8), pages 869-887, December.
    3. Antonio Romero-Medina & Katari´na Cechlárová, 2001. "Stability in coalition formation games," International Journal of Game Theory, Springer;Game Theory Society, vol. 29(4), pages 487-494.
    4. Ballester, Coralio, 2004. "NP-completeness in hedonic games," Games and Economic Behavior, Elsevier, vol. 49(1), pages 1-30, October.
    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. Tayfun Sönmez & Suryapratim Banerjee & Hideo Konishi, 2001. "Core in a simple coalition formation game," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 18(1), pages 135-153.
    7. Dreze, J H & Greenberg, J, 1980. "Hedonic Coalitions: Optimality and Stability," Econometrica, Econometric Society, vol. 48(4), pages 987-1003, May.
    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.
    9. Burani, Nadia & Zwicker, William S., 2003. "Coalition formation games with separable preferences," Mathematical Social Sciences, Elsevier, vol. 45(1), pages 27-52, February.
    10. Ray, Debraj, 1989. "Credible Coalitions and the Core," International Journal of Game Theory, Springer;Game Theory Society, vol. 18(2), pages 185-187.
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    Cited by:

    1. Dinko Dimitrov & Peter Borm & Ruud Hendrickx & Shao Sung, 2006. "Simple Priorities and Core Stability in Hedonic Games," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 26(2), pages 421-433, April.
    2. Carmelo Rodríguez-Álvarez, 2009. "Strategy-proof coalition formation," International Journal of Game Theory, Springer;Game Theory Society, vol. 38(3), pages 431-452, November.
    3. Karakaya, Mehmet, 2011. "Hedonic coalition formation games: A new stability notion," Mathematical Social Sciences, Elsevier, vol. 61(3), pages 157-165, May.
    4. Alison Watts, 2007. "Formation of segregated and integrated groups," International Journal of Game Theory, Springer;Game Theory Society, vol. 35(4), pages 505-519, April.
    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. Woeginger, Gerhard J., 2013. "A hardness result for core stability in additive hedonic games," Mathematical Social Sciences, Elsevier, vol. 65(2), pages 101-104.
    7. Alison Watts, 2006. "Formation of Segregated and Integrated Groups," Working Papers 2006.127, Fondazione Eni Enrico Mattei.
    8. repec:spr:jogath:v:46:y:2017:i:4:d:10.1007_s00182-016-0561-7 is not listed on IDEAS
    9. Dinko Dimitrov & Shao Chin Sung, 2006. "A Taxonomy of Myopic Stability Concepts for Hedonic Games," Working Papers 2006.10, Fondazione Eni Enrico Mattei.
    10. José Alcantud & Ritxar Arlegi, 2012. "An axiomatic analysis of ranking sets under simple categorization," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 3(1), pages 227-245, March.
    11. Vincent Iehlé, 2005. "The core-partition of hedonic games," Cahiers de la Maison des Sciences Economiques b05091, Université Panthéon-Sorbonne (Paris 1).
    12. Kleinberg, Jon & Ligett, Katrina, 2013. "Information-sharing in social networks," Games and Economic Behavior, Elsevier, vol. 82(C), pages 702-716.
    13. 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.
    14. Suksompong, Warut, 2015. "Individual and group stability in neutral restrictions of hedonic games," Mathematical Social Sciences, Elsevier, vol. 78(C), pages 1-5.
    15. Dinko Dimitrov & Shao Chin Sung, 2011. "Size Monotonicity and Stability of the Core in Hedonic Games," Working Papers 2011.52, Fondazione Eni Enrico Mattei.
    16. Iehle, Vincent, 2007. "The core-partition of a hedonic game," Mathematical Social Sciences, Elsevier, vol. 54(2), pages 176-185, September.
    17. Arlegi, Ritxar & Dimitrov, Dinko, 2016. "Power set extensions of dichotomous preferences," Mathematical Social Sciences, Elsevier, vol. 83(C), pages 20-29.
    18. 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.
    19. Mehmet Karakaya & Bettina Klaus, 2017. "Hedonic coalition formation games with variable populations: core characterizations and (im)possibilities," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(2), pages 435-455, May.
    20. Antoni Rubí-Barceló, 2013. "Efficiency and stability in a strategic model of hedonic coalitions," International Journal of Economic Theory, The International Society for Economic Theory, vol. 9(2), pages 131-145, June.

    More about this item

    Keywords

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

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • A14 - General Economics and Teaching - - General Economics - - - Sociology of Economics
    • D20 - Microeconomics - - Production and Organizations - - - General

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