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Submodularity of some classes of the combinatorial optimization games

Author

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  • Yoshio Okamoto

Abstract

Submodularity (or concavity) is considered as an important property in the field of cooperative game theory. In this article, we characterize submodular minimum coloring games and submodular minimum vertex cover games. These characterizations immediately show that it can be decided in polynomial time that the minimum coloring game or the minimum vertex cover game on a given graph is submodular or not. Related to these results, the Shapley values are also investigated. Copyright Springer-Verlag 2003

Suggested Citation

  • 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.
    • Handle: RePEc:spr:mathme:v:58:y:2003:i:1:p:131-139
    DOI: 10.1007/s001860300284
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    Citations

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    Cited by:

    1. Hamers, H.J.M. & Josune Albizuri, M., 2013. "Graphs Inducing Totally Balanced and Submodular Chinese Postman Games," Other publications TiSEM b1fbd78c-1207-4d55-8313-2, Tilburg University, School of Economics and Management.
    2. Trine Platz & Herbert Hamers, 2015. "On games arising from multi-depot Chinese postman problems," Annals of Operations Research, Springer, vol. 235(1), pages 675-692, December.
    3. 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.
    4. Sergei Dotsenko & Vladimir Mazalov, 2021. "A Cooperative Network Packing Game with Simple Paths," Mathematics, MDPI, vol. 9(14), pages 1-18, July.
    5. Hamers, H.J.M. & Josune Albizuri, M., 2013. "Graphs Inducing Totally Balanced and Submodular Chinese Postman Games," Discussion Paper 2013-006, Tilburg University, Center for Economic Research.
    6. Hamers, H.J.M. & Miquel, S. & Norde, H.W., 2011. "Monotonic Stable Solutions for Minimum Coloring Games," Other publications TiSEM efae8d09-83e6-4fe4-9623-e, Tilburg University, School of Economics and Management.
    7. Thomas Bietenhader & Yoshio Okamoto, 2006. "Core Stability of Minimum Coloring Games," Mathematics of Operations Research, INFORMS, vol. 31(2), pages 418-431, May.
    8. Stefano Moretti & Henk Norde, 2022. "Some new results on generalized additive games," International Journal of Game Theory, Springer;Game Theory Society, vol. 51(1), pages 87-118, March.
    9. Hamers, Herbert & Horozoglu, Nayat & Norde, Henk & Platz, Trine Tornoe, 2022. "On the properties of weighted minimum colouring games," Other publications TiSEM ee84d5e4-08d7-4154-9521-2, Tilburg University, School of Economics and Management.
    10. Herbert Hamers & Nayat Horozoglu & Henk Norde & Trine Tornøe Platz, 2022. "On the properties of weighted minimum colouring games," Annals of Operations Research, Springer, vol. 318(2), pages 963-983, November.
    11. Hamers, H.J.M. & Miquel, S. & Norde, H.W., 2011. "Monotonic Stable Solutions for Minimum Coloring Games," Discussion Paper 2011-016, Tilburg University, Center for Economic Research.

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