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Nondominated Equilibrium Solutions of a Multiobjective Two-Person Nonzero-Sum Game and Corresponding Mathematical Programming Problem

Author

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  • I. Nishizaki

    (Hiroshima University)

  • T. Notsu

    (Hiroshima University)

Abstract

With reference to a multiobjective two-person nonzero-sum game, we define nondominated equilibrium solutions and provide a necessary and sufficient condition for a pair of mixed strategies to be a nondominated equilibrium solution. Using the necessary and sufficient condition, we formulate a mathematical programming problem yielding nondominated equilibrium solutions. We give a numerical example and demonstrate that nondominated equilibrium solutions can be obtained by solving the formulated mathematical programming problem.

Suggested Citation

  • I. Nishizaki & T. Notsu, 2007. "Nondominated Equilibrium Solutions of a Multiobjective Two-Person Nonzero-Sum Game and Corresponding Mathematical Programming Problem," Journal of Optimization Theory and Applications, Springer, vol. 135(2), pages 217-239, November.
    • Handle: RePEc:spr:joptap:v:135:y:2007:i:2:d:10.1007_s10957-007-9245-6
    DOI: 10.1007/s10957-007-9245-6
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    References listed on IDEAS

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    1. Borm, Peter & Vermeulen, Dries & Voorneveld, Mark, 2003. "The structure of the set of equilibria for two person multicriteria games," European Journal of Operational Research, Elsevier, vol. 148(3), pages 480-493, August.
    2. Zhao, Jingang, 1991. "The Equilibria of a Multiple Object Game," International Journal of Game Theory, Springer;Game Theory Society, vol. 20(2), pages 171-182.
    3. Voorneveld, Mark & Vermeulen, Dries & Borm, Peter, 1999. "Axiomatizations of Pareto Equilibria in Multicriteria Games," Games and Economic Behavior, Elsevier, vol. 28(1), pages 146-154, July.
    4. Mark Voorneveld & Sofia Grahn & Martin Dufwenberg, 2000. "Ideal equilibria in noncooperative multicriteria games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 52(1), pages 65-77, September.
    5. Norde, Henk & Potters, Jos & Reijnierse, Hans & Vermeulen, Dries, 1996. "Equilibrium Selection and Consistency," Games and Economic Behavior, Elsevier, vol. 12(2), pages 219-225, February.
    6. M. Voorneveld, 1999. "Pareto-Optimal Security Strategies as Minimax Strategies of a Standard Matrix Game," Journal of Optimization Theory and Applications, Springer, vol. 102(1), pages 203-210, July.
    7. ZHAO, Jingang, 1991. "The equilibria of a multiple objective game," LIDAM Reprints CORE 987, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    Cited by:

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    2. Hadi Charkhgard & Martin Savelsbergh & Masoud Talebian, 2018. "Nondominated Nash points: application of biobjective mixed integer programming," 4OR, Springer, vol. 16(2), pages 151-171, June.

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