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

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  • Koczy, Laszlo A.
  • Lauwers, Luc

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.
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Suggested Citation

  • Koczy, Laszlo A. & Lauwers, Luc, 2007. "The minimal dominant set is a non-empty core-extension," Games and Economic Behavior, Elsevier, vol. 61(2), pages 277-298, November.
  • Handle: RePEc:eee:gamebe:v:61:y:2007:i:2:p:277-298
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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. Yang, Yi-You, 2010. "On the accessibility of the core," Games and Economic Behavior, Elsevier, vol. 69(1), pages 194-199, May.
    2. 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.
    3. 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.

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    JEL classification:

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

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