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The minimal dominant set is a non-empty core-extension

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  • László Á. Kóczy

    (Catholic University Leuven)

Abstract

A set of outcomes for a TU-game in characteristic function form is dominant if it is, with respect to an outsider-independent dominance relation, accessible (or admissible) and closed. This outsider-independent dominance relation is restrictive in the sense that a deviating coalition cannot determine the payoffs of those coalitions that are not involved in the deviation. The minimal (for inclusion) dominant set is non-empty and for a game with a non-empty coalition structure core, the minimal dominant set returns this core.

Suggested Citation

  • László Á. Kóczy, 2002. "The minimal dominant set is a non-empty core-extension," Economics Bulletin, AccessEcon, vol. 28(8), pages 1.
    • Handle: RePEc:ebl:ecbull:eb-02aa0011
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    References listed on IDEAS

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    1. Sengupta, Abhijit & Sengupta, Kunal, 1996. "A Property of the Core," Games and Economic Behavior, Elsevier, vol. 12(2), pages 266-273, February.
    2. Sengupta, Abhijit & Sengupta, Kunal, 1994. "Viable Proposals," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 35(2), pages 347-359, May.
    3. Koczy, Laszlo A. & Lauwers, Luc, 2004. "The coalition structure core is accessible," Games and Economic Behavior, Elsevier, vol. 48(1), pages 86-93, July.
    4. Kalai, Ehud & Schmeidler, David, 1977. "An admissible set occurring in various bargaining situations," Journal of Economic Theory, Elsevier, vol. 14(2), pages 402-411, April.
    5. Greenberg, Joseph, 1994. "Coalition structures," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 2, chapter 37, pages 1305-1337, Elsevier.
    6. Zhou Lin, 1994. "A New Bargaining Set of an N-Person Game and Endogenous Coalition Formation," Games and Economic Behavior, Elsevier, vol. 6(3), pages 512-526, May.
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    Cited by:

    1. Gedai, Endre & Kóczy, László Á. & Zombori, Zita, 2012. "Cluster games: A novel, game theory-based approach to better understand incentives and stability in clusters," MPRA Paper 65095, University Library of Munich, Germany.
    2. David Pérez-Castrillo & Marilda Sotomayor, 2023. "Constrained-optimal tradewise-stable outcomes in the one-sided assignment game: a solution concept weaker than the core," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 76(3), pages 963-994, October.
    3. László Á. Kóczy, 2018. "Partition Function Form Games," Theory and Decision Library C, Springer, number 978-3-319-69841-0, March.
    4. Csoka, Peter & Herings, P. Jean-Jacques & Koczy, Laszlo A., 2007. "Coherent measures of risk from a general equilibrium perspective," Journal of Banking & Finance, Elsevier, vol. 31(8), pages 2517-2534, August.
    5. Kóczy Á., László, 2006. "A Neumann-féle játékelmélet [Neumanns game theory]," Közgazdasági Szemle (Economic Review - monthly of the Hungarian Academy of Sciences), Közgazdasági Szemle Alapítvány (Economic Review Foundation), vol. 0(1), pages 31-45.
    6. Yang, Yi-You, 2011. "Accessible outcomes versus absorbing outcomes," Mathematical Social Sciences, Elsevier, vol. 62(1), pages 65-70, July.
    7. Yi-You Yang, 2020. "On the characterizations of viable proposals," Theory and Decision, Springer, vol. 89(4), pages 453-469, November.
    8. Gabor Virag, 2006. "Outside offers and bidding costs," CERS-IE WORKING PAPERS 0610, Institute of Economics, Centre for Economic and Regional Studies, revised 30 Aug 2006.
    9. 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.
    10. 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.
    11. Yang, Yi-You, 2010. "On the accessibility of the core," Games and Economic Behavior, Elsevier, vol. 69(1), pages 194-199, May.
    12. 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.
    13. Iván Major, 2006. "Why do (or do not) banks share customer information? A comparison of mature private credit markets and markets in transition," CERS-IE WORKING PAPERS 0603, Institute of Economics, Centre for Economic and Regional Studies, revised 24 Apr 2006.
    14. András Simonovits, 2006. "Social Security Reform in the US: Lessons from Hungary," CERS-IE WORKING PAPERS 0602, Institute of Economics, Centre for Economic and Regional Studies, revised 24 Apr 2006.

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    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory

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