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Simple and three-valued simple minimum coloring games

Author

Listed:
  • M. Musegaas

    (Tilburg University)

  • P. E. M. Borm

    (Tilburg University)

  • M. Quant

    (Tilburg University)

Abstract

In this paper minimum coloring games are considered. We characterize the class of conflict graphs inducing simple or three-valued simple minimum coloring games. We provide an upper bound on the number of maximum cliques of conflict graphs inducing such games. Moreover, a characterization of the core is provided in terms of the underlying conflict graph. In particular, in case of a perfect conflict graph the core of an induced three-valued simple minimum coloring game equals the vital core.

Suggested Citation

  • M. Musegaas & P. E. M. Borm & M. Quant, 2016. "Simple and three-valued simple minimum coloring games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 84(2), pages 239-258, October.
    • Handle: RePEc:spr:mathme:v:84:y:2016:i:2:d:10.1007_s00186-016-0542-4
    DOI: 10.1007/s00186-016-0542-4
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    References listed on IDEAS

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    1. M. Musegaas & P. E. M. Borm & M. Quant, 2018. "Three-valued simple games," Theory and Decision, Springer, vol. 85(2), pages 201-224, August.
    2. Peter Borm & Herbert Hamers & Ruud Hendrickx, 2001. "Operations research games: A survey," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 9(2), pages 139-199, December.
    3. Thomas Bietenhader & Yoshio Okamoto, 2006. "Core Stability of Minimum Coloring Games," Mathematics of Operations Research, INFORMS, vol. 31(2), pages 418-431, May.
    4. Shapley, L. S. & Shubik, Martin, 1954. "A Method for Evaluating the Distribution of Power in a Committee System," American Political Science Review, Cambridge University Press, vol. 48(3), pages 787-792, September.
    5. Xiaotie Deng & Toshihide Ibaraki & Hiroshi Nagamochi, 1999. "Algorithmic Aspects of the Core of Combinatorial Optimization Games," Mathematics of Operations Research, INFORMS, vol. 24(3), pages 751-766, August.
    6. Yoshio Okamoto, 2003. "Submodularity of some classes of the combinatorial optimization games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 58(1), pages 131-139, September.
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    Cited by:

    1. M. Musegaas & P. E. M. Borm & M. Quant, 2018. "Three-valued simple games," Theory and Decision, Springer, vol. 85(2), pages 201-224, August.
    2. Miles, Sandra Jeanquart & McCamey, Randy, 2018. "The candidate experience: Is it damaging your employer brand?," Business Horizons, Elsevier, vol. 61(5), pages 755-764.

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    More about this item

    Keywords

    Minimum coloring games; Simple games; Three-valued simple games;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory

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