Title: Characterization of Nash Equilibrium Strategy for Heptagonal Fuzzy Games
Author(s): F. Madandar, S. Haghayeghi, S. M. Vaezpour
Pages: 353-367
Cite as:
F. Madandar, S. Haghayeghi, S. M. Vaezpour, Characterization of Nash Equilibrium Strategy for Heptagonal Fuzzy Games, Int. J. Anal. Appl., 16 (3) (2018), 353-367.


In this paper, the Nash equilibrium strategy of two-person zero-sum games with heptagonal fuzzy payoffs is considered and the existence of Nash equilibrium strategy is studied. Also, based on the fuzzy max order several models in heptagonal fuzzy environment is constructed and the existence of their equilibrium strategies is proposed. In the sequel, the existence of Pareto Nash equilibrium strategies and weak Pareto Nash equilibrium strategies is investigated for fuzzy matrix games. Finally, the relation between Pareto Nash equilibrium strategy and parametric bi-matrix games is established.

Full Text: PDF



  1. C. R. Bector, S. Chandra, Fuzzy Mathematical Programming and Fuzzy Matrix Games, springer, Berlin, 2005. Google Scholar

  2. L. Campos, Fuzzy linear programming model to solve fuzzy matrix game, Fuzzy Sets Syst., 32(3)(1989), 275-289. Google Scholar

  3. Bapi Dutta, S. K. Gupta, On Nash equilibrium strategy of two-person zero-sum games with Trapezoidal fuzzy payoffs, Fuzzy Inf. Eng., 6(3)(2014), 299-314. Google Scholar

  4. Li Cunlin, Zhang Qiang, Nash equilibrium strategy for fuzzy non-cooperative games, Fuzzy Sets Syst., 176(1)(2011), 46-55. Google Scholar

  5. B. Liu, Uncertain programming. New York:wiley, 1999. Google Scholar

  6. B. Liu , Uncertainty theory. An introduction to its axiomatic foundations, Studies in Fuzziness and Soft Computing, 154, Springer-Verlag, Berlin, 2004. Google Scholar

  7. T. Maeda ,On characterization of equilibrium strategy of bimatrix games with fuzzy payoffs, J. Math. Anal. Appl., 251(2)(2000), 885-896. Google Scholar

  8. J. F Nash, Non-cooperative games , Ann. Math, 54(2)(1951), 286-295. Google Scholar

  9. J. von Neumann, O. Morgenstern, Theory of Games and Economic Behavior, Princeton University Press, Princeton, New Jersey, 1944. Google Scholar

  10. K. Rathi, S. Balamohan, Representation and Ranking of fuzzy numbers with Heptagonal membership function using value and Ambiguity index, Appl. Math. Sci., 87(8)(2014), 4309-4321. Google Scholar

  11. J. Ramik, J. R imanek, Inequality relation between fuzzy numbers and its use in fuzzy optimization, Fuzzy Sets Syst., 16(2)(1985), 123-138. Google Scholar

  12. M. Sakawa, Fuzzy Sets and Interactive Multiobjective Optimization, Plenum Press, New York, 1993. Google Scholar

  13. A. V. Yazenin, Fuzzy and stochastic programming, Fuzzy Sets Syst., 22(1-2)(1987), 171-180. Google Scholar

  14. L. A. Zadeh, Fuzzy sets, Information and Control, (8)(1965), 338-353. Google Scholar

  15. L. A. Zadeh, Fuzzy set as a basis for a theory of possibility, Fuzzy Sets Syst., 1(1978), 3-28. Google Scholar

  16. H. J. Zimmermann, Application of fuzzy set theory to mathematical programming, Inform. Sci., 36(1-2)(1985), 29-58. Google Scholar

  17. H. J. Zimmermann, Fuzzy Set Theory and its Applications, Second edition, Kluwer Academic Publishers, Boston, MA, 1992. Google Scholar


Copyright © 2021 IJAA, unless otherwise stated.