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Multicriteria Goal Games

Author

Listed:
  • F. R. Fernández

    (Universidad de Sevilla)

  • L. Monroy

    (Universidad de Sevilla)

  • J. Puerto

    (Universidad de Sevilla)

Abstract

In this paper, we deal with multicriteria matrix games. Different solution concepts have been proposed to cope with these games. Recently, the concept of Pareto-optimal security strategy which assures the property of security in the individual criteria against an opponent's deviation in strategy has been introduced. However, the idea of security behind this concept is based on expected values, so that this security might be violated by mixed strategies when replications are not allowed. To avoid this inconvenience, we propose in this paper a new concept of solution for these games: the G-goal security strategy, which includes as part of the solution the probability of obtaining prespecified values in the payoff functions. Thus, attitude toward risk together with payoff values are considered jointly in the solution analysis.

Suggested Citation

  • F. R. Fernández & L. Monroy & J. Puerto, 1998. "Multicriteria Goal Games," Journal of Optimization Theory and Applications, Springer, vol. 99(2), pages 403-421, November.
    • Handle: RePEc:spr:joptap:v:99:y:1998:i:2:d:10.1023_a:1021726311384
    DOI: 10.1023/A:1021726311384
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    References listed on IDEAS

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    1. Yano, Hitoshi & Sakawa, Masatoshi, 1989. "A unified approach for characterizing Pareto optimal solutions of multiobjective optimization problems: The hyperplane method," European Journal of Operational Research, Elsevier, vol. 39(1), pages 61-70, March.
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    Cited by:

    1. Andreas H. Hamel & Andreas Löhne, 2018. "A set optimization approach to zero-sum matrix games with multi-dimensional payoffs," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 88(3), pages 369-397, December.
    2. Monroy, Luisa & Fernández, Francisco R., 2011. "The Shapley-Shubik index for multi-criteria simple games," European Journal of Operational Research, Elsevier, vol. 209(2), pages 122-128, March.
    3. F. R. Fernández & M. A. Hinojosa & J. Puerto, 2002. "Core Solutions in Vector-Valued Games," Journal of Optimization Theory and Applications, Springer, vol. 112(2), pages 331-360, February.
    4. Kroenke, Adriana & Wilhelm, Volmir Eugênio, 2017. "Jogos Vetoriais no Posicionamento Contábil de Empresas de Siderurgia e Metalurgia Listadas no BM&FBOVESPA," Revista Brasileira de Economia - RBE, EPGE Brazilian School of Economics and Finance - FGV EPGE (Brazil), vol. 71(4), December.
    5. Fernandez, F. R. & Hinojosa, M. A. & Puerto, J., 2004. "Set-valued TU-games," European Journal of Operational Research, Elsevier, vol. 159(1), pages 181-195, November.

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