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A Cooperative Network Packing Game with Simple Paths

Author

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  • Sergei Dotsenko

    (Faculty of Information Technology, Taras Shevchenko National University of Kyiv, Gavrilishina Str. 24, 04116 Kyiv, Ukraine
    These authors contributed equally to this work.)

  • Vladimir Mazalov

    (Institute of Applied Mathematical Research, Karelian Research Center of the Russian Academy of Sciences, Pushkinskaya Str. 11, 185910 Petrozavodsk, Russia
    Faculty of Applied Mathematics-Control Processes, Saint-Petersburg State University, 7/9 Universitetskaya nab., 199034 Saint Petersburg, Russia
    These authors contributed equally to this work.)

Abstract

We consider a cooperative packing game in which the characteristic function is defined as the maximum number of independent simple paths of a fixed length included in a given coalition. The conditions under which the core exists in this game are established, and its form is obtained. For several particular graphs, the explicit form of the core is presented.

Suggested Citation

  • Sergei Dotsenko & Vladimir Mazalov, 2021. "A Cooperative Network Packing Game with Simple Paths," Mathematics, MDPI, vol. 9(14), pages 1-18, July.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:14:p:1683-:d:596198
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    References listed on IDEAS

    as
    1. Jackson, Matthew O. & Wolinsky, Asher, 1996. "A Strategic Model of Social and Economic Networks," Journal of Economic Theory, Elsevier, vol. 71(1), pages 44-74, October.
    2. Roger B. Myerson, 1977. "Graphs and Cooperation in Games," Mathematics of Operations Research, INFORMS, vol. 2(3), pages 225-229, August.
    3. 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.
    4. Xiaotie Deng & Qizhi Fang & Xiaoxun Sun, 2009. "Finding nucleolus of flow game," Journal of Combinatorial Optimization, Springer, vol. 18(1), pages 64-86, July.
    5. Gusev, Vasily V., 2020. "The vertex cover game: Application to transport networks," Omega, Elsevier, vol. 97(C).
    6. Gérard Hamiache, 2001. "The Owen value values friendship," International Journal of Game Theory, Springer;Game Theory Society, vol. 29(4), pages 517-532.
    7. 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.
    8. Thomas Bietenhader & Yoshio Okamoto, 2006. "Core Stability of Minimum Coloring Games," Mathematics of Operations Research, INFORMS, vol. 31(2), pages 418-431, May.
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