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Pareto-Optimal Security Strategies as Minimax Strategies of a Standard Matrix Game

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  • M. Voorneveld

    (Tilburg University)

Abstract

We prove that, in a multicriteria matrix game, a strategy is a Pareto-optimal security strategy if and only if it is a minimax strategy of a standard matrix game that is obtained by a suitable weighting of the criteria.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:102:y:1999:i:1:d:10.1023_a:1021854814980
    DOI: 10.1023/A:1021854814980
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    References listed on IDEAS

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    1. Borm, Peter & Garcia-Jurado, Ignacio & Potters, Jos & Tijs, Stef, 1996. "An amalgation of games," European Journal of Operational Research, Elsevier, vol. 89(3), pages 570-580, March.
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    Cited by:

    1. Karima Fahem & Mohammed Radjef, 2015. "Properly efficient Nash equilibrium in multicriteria noncooperative games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 82(2), pages 175-193, October.
    2. 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.
    3. 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.
    4. A. Zapata & A. M. Mármol & L. Monroy & M. A. Caraballo, 2019. "A Maxmin Approach for the Equilibria of Vector-Valued Games," Group Decision and Negotiation, Springer, vol. 28(2), pages 415-432, April.
    5. Naouel Yousfi-Halimi & Mohammed Said Radjef & Hachem Slimani, 2018. "Refinement of pure Pareto Nash equilibria in finite multicriteria games using preference relations," Annals of Operations Research, Springer, vol. 267(1), pages 607-628, August.
    6. Stefan Rass & Sandra König & Stefan Schauer, 2017. "Defending Against Advanced Persistent Threats Using Game-Theory," PLOS ONE, Public Library of Science, vol. 12(1), pages 1-43, January.

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