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

Author

Listed:
  • Laszlo A. Koczy

    (Department of Economics, University of Maastricht)

  • Luc Lauwers

    (Centre for Economic Studies, Katholieke Universiteit Leuven)

Abstract
A set of outcomes for a transferable utility 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. We provide an algorithm to find the minimal dominant set.

Suggested Citation

  • Laszlo A. Koczy & Luc Lauwers, 2004. "The minimal dominant set is a non-empty core-extension," CERS-IE WORKING PAPERS 0421, Institute of Economics, Centre for Economic and Regional Studies.
    • Handle: RePEc:has:discpr:0421
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    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. 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.
    2. 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.
    3. Yang, Yi-You, 2010. "On the accessibility of the core," Games and Economic Behavior, Elsevier, vol. 69(1), pages 194-199, May.
    4. 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.
    5. 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.
    6. László Á. Kóczy, 2018. "Partition Function Form Games," Theory and Decision Library C, Springer, number 978-3-319-69841-0, December.
    7. 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.
    8. Yi-You Yang, 2020. "On the characterizations of viable proposals," Theory and Decision, Springer, vol. 89(4), pages 453-469, November.
    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. 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.
    12. 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.
    13. Yang, Yi-You, 2011. "Accessible outcomes versus absorbing outcomes," Mathematical Social Sciences, Elsevier, vol. 62(1), pages 65-70, July.
    14. 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.

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    More about this item

    Keywords

    dynamic solution; absorbing set; core; non-emptiness;
    All these keywords.

    JEL classification:

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

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