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Accessibility and stability of the coalition structure core

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  • Sylvain Béal
  • Eric Rémila
  • Philippe Solal

Abstract

This article shows that, for any transferable utility game in coalitional form with a nonempty coalition structure core, the number of steps required to switch from a payoff configuration out of the coalition structure core to a payoff configuration in the coalition structure core is less than or equal to $$(n^2+4n)/4$$ , where $$n$$ is the cardinality of the player set. This number improves the upper bounds found so far. We also provide a sufficient condition for the stability of the coalition structure core, i.e. a condition which ensures the accessibility of the coalition structure core in one step. On the class of simple games, this sufficient condition is also necessary and has a meaningful interpretation. Copyright Springer-Verlag Berlin Heidelberg 2013

Suggested Citation

  • Sylvain Béal & Eric Rémila & Philippe Solal, 2013. "Accessibility and stability of the coalition structure core," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 78(2), pages 187-202, October.
    • Handle: RePEc:spr:mathme:v:78:y:2013:i:2:p:187-202
    DOI: 10.1007/s00186-013-0439-4
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    References listed on IDEAS

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    1. Béal, Sylvain & Rémila, Eric & Solal, Philippe, 2013. "An optimal bound to access the core in TU-games," Games and Economic Behavior, Elsevier, vol. 80(C), pages 1-9.
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    5. Béal, Sylvain & Rémila, Eric & Solal, Philippe, 2010. "On the number of blocks required to access the core," MPRA Paper 26578, University Library of Munich, Germany.
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    7. Koczy, Laszlo A. & Lauwers, Luc, 2004. "The coalition structure core is accessible," Games and Economic Behavior, Elsevier, vol. 48(1), pages 86-93, July.
    8. Koczy, Laszlo A., 2006. "The core can be accessed with a bounded number of blocks," Journal of Mathematical Economics, Elsevier, vol. 43(1), pages 56-64, December.
    9. Yang, Yi-You, 2010. "On the accessibility of the core," Games and Economic Behavior, Elsevier, vol. 69(1), pages 194-199, May.
    10. Yang, Yi-You, 2011. "Accessible outcomes versus absorbing outcomes," Mathematical Social Sciences, Elsevier, vol. 62(1), pages 65-70, July.
    11. Kamal Jain & Rakesh Vohra, 2010. "Extendability and von Neuman–Morgenstern stability of the core," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(4), pages 691-697, October.
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    13. Thomas Bietenhader & Yoshio Okamoto, 2006. "Core Stability of Minimum Coloring Games," Mathematics of Operations Research, INFORMS, vol. 31(2), pages 418-431, May.
    14. T. E. S. Raghavan & Tamás Solymosi, 2001. "Assignment games with stable core," International Journal of Game Theory, Springer;Game Theory Society, vol. 30(2), pages 177-185.
    15. Manea, Mihai, 2007. "Core tatonnement," Journal of Economic Theory, Elsevier, vol. 133(1), pages 331-349, March.
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    Cited by:

    1. Herings, P. Jean-Jacques & Kóczy, László Á., 2021. "The equivalence of the minimal dominant set and the myopic stable set for coalition function form games," Games and Economic Behavior, Elsevier, vol. 127(C), pages 67-79.
    2. Bando, Keisuke & Kawasaki, Ryo, 2021. "Stability properties of the core in a generalized assignment problem," Games and Economic Behavior, Elsevier, vol. 130(C), pages 211-223.
    3. Mauleon, Ana & Roehl, Nils & Vannetelbosch, Vincent, 2019. "Paths to stability for overlapping group structures," Journal of Mathematical Economics, Elsevier, vol. 83(C), pages 19-24.
    4. Yi-You Yang, 2020. "On the characterizations of viable proposals," Theory and Decision, Springer, vol. 89(4), pages 453-469, November.
    5. Péter Szikora, 2013. "Introduction into the literature of cooperative game theory with special emphasis on dynamic games and the core," Proceedings- 11th International Conference on Mangement, Enterprise and Benchmarking (MEB 2013),, Óbuda University, Keleti Faculty of Business and Management.

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