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The Minimal Dominant Set is a Non-Empty Core-Extension

Author

Listed:
  • László Á. Kóczy
  • Luc Lauwers

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 & Luc Lauwers, 2002. "The Minimal Dominant Set is a Non-Empty Core-Extension," Working Papers of Department of Economics, Leuven ces0220, KU Leuven, Faculty of Economics and Business (FEB), Department of Economics, Leuven.
    • Handle: RePEc:ete:ceswps:ces0220
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    2. Yang, Yi-You, 2010. "On the accessibility of the core," Games and Economic Behavior, Elsevier, vol. 69(1), pages 194-199, May.
    3. 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.
    4. László Á. Kóczy, 2018. "Partition Function Form Games," Theory and Decision Library C, Springer, number 978-3-319-69841-0, December.
    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. Yi-You Yang, 2020. "On the characterizations of viable proposals," Theory and Decision, Springer, vol. 89(4), pages 453-469, November.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. Yang, Yi-You, 2011. "Accessible outcomes versus absorbing outcomes," Mathematical Social Sciences, Elsevier, vol. 62(1), pages 65-70, July.
    12. 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.
    13. 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.
    14. 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.
    15. 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.

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    JEL classification:

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

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