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Two-person non-zero-sum gamesas multicriteria goal games

Author

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  • F.R. Fernández
  • J. Puerto
  • L. Monroy

Abstract

In this paper, we propose a new way to analyze bimatrix games. This new approach consists of considering the game as a bicriteria matrix game. The solution concepts behind this game are based on getting the probability to achieve some prespecified goals. We consider as a part of the solution, not only the payoff values, but also the probability to get them. In addition, to avoid the choice of only one goal, two different approaches are used. Firstly, sensitivity analysis of the solution set is carried out on the range of goals, secondly a partition of the goal space in a finite number of regions is presented. Some examples are included to illustrate the results in the paper. Copyright Kluwer Academic Publishers 1998

Suggested Citation

  • F.R. Fernández & J. Puerto & L. Monroy, 1998. "Two-person non-zero-sum gamesas multicriteria goal games," Annals of Operations Research, Springer, vol. 84(0), pages 195-208, December.
    • Handle: RePEc:spr:annopr:v:84:y:1998:i:0:p:195-208:10.1023/a:1018988804013
    DOI: 10.1023/A:1018988804013
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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. 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.
    3. 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.
    4. 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.
    5. Richárd Kicsiny & Zoltán Varga, 2023. "New algorithm for checking Pareto optimality in bimatrix games," Annals of Operations Research, Springer, vol. 320(1), pages 235-259, January.

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