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The structure of the set of equilibria for two person multicriteria games


  • Borm, Peter
  • Vermeulen, Dries
  • Voorneveld, Mark


In this paper the structure of the set of equilibria for two person multicriteria games is analysed. It turns out that the classical result for the set of equilibria for bimatrix games, that it is a finite union of polytopes, is only valid for multicriteria games if one of the players only has two pure strategies. A full polyhedral description of these polytopes can be derived when the player with an arbitrary number of pure strategies has one criterion.
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Suggested Citation

  • 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.
  • Handle: RePEc:eee:ejores:v:148:y:2003:i:3:p:480-493

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    References listed on IDEAS

    1. Blume, Lawrence E & Zame, William R, 1994. "The Algebraic Geometry of Perfect and Sequential Equilibrium," Econometrica, Econometric Society, vol. 62(4), pages 783-794, July.
    2. D. Blackwell, 2010. "An Analog of the Minmax Theorem for Vector Payoffs," Levine's Working Paper Archive 466, David K. Levine.
    3. Borm, P.E.M. & Tijs, S.H. & van den Aarssen, J.C.M., 1988. "Pareto equilibria in multiobjective games," Other publications TiSEM a02573c0-8c7e-409d-bc75-0, Tilburg University, School of Economics and Management.
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    Cited by:

    1. Tim Schulteis & Andres Perea & Hans Peters & Dries Vermeulen, 2007. "Revision of conjectures about the opponent’s utilities in signaling games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 30(2), pages 373-384, February.
    2. Luisa Monroy & Amparo M. Mármol & Victoriana Rubiales, 2005. "A bargaining model for finite n-person multi-criteria games," Economic Working Papers at Centro de Estudios Andaluces E2005/21, Centro de Estudios Andaluces.

    More about this item

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games


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