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Universally Balanced Combinatorial Optimization Games

Author

Listed:
  • Gabrielle Demange

    (PSE - Paris-Jourdan Sciences Economiques - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - INRA - Institut National de la Recherche Agronomique - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

  • Xiaotie Deng

    (Department of Computer Science [Hong Kong] - CUHK - City University of Hong Kong [Hong Kong])

Abstract

This article surveys studies on universally balanced properties of cooperative games defined in a succinct form. In particular, we focus on combinatorial optimization games in which the values to coalitions are defined through linear optimization programs, possibly combinatorial, that is subject to integer constraints. In economic settings, the integer requirement reflects some forms of indivisibility. We are interested in the classes of games that guarantee a non-empty core no matter what are the admissible values assigned to the parameters defining these programs. We call such classes universally balanced. We present characterization and complexity results on the universally balancedness property for some classes of interesting combinatorial optimization games. In particular, we focus on the algorithmic properties for identifying universally balancedness for the games under discussion.

Suggested Citation

  • Gabrielle Demange & Xiaotie Deng, 2010. "Universally Balanced Combinatorial Optimization Games," PSE-Ecole d'économie de Paris (Postprint) halshs-00670891, HAL.
    • Handle: RePEc:hal:pseptp:halshs-00670891
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    References listed on IDEAS

    as
    1. Le Breton, M & Owen, G & Weber, S, 1992. "Strongly Balanced Cooperative Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 20(4), pages 419-427.
    2. van Velzen, S., 2005. "Simple Combinatorial Optimisation Cost Games," Other publications TiSEM 68df1061-50bc-43bf-b79c-a, Tilburg University, School of Economics and Management.
    3. van Velzen, S., 2005. "Simple Combinatorial Optimisation Cost Games," Discussion Paper 2005-118, Tilburg University, Center for Economic Research.
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    More about this item

    Keywords

    combinatorial cooperative games; balanced; blocking; core; integrality;
    All these keywords.

    JEL classification:

    • C - Mathematical and Quantitative Methods
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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