Journal of Applied Mathematics
Volume 2012 (2012), Article ID 824790, 15 pages
Research Article

Characterization of the Equilibrium Strategy of Fuzzy Bimatrix Games Based on 𝐿 - 𝑅 Fuzzy Variables

School of Management, Beifang University of Nationalities, Yinchuan 750021, China

Received 25 February 2012; Accepted 30 March 2012

Academic Editor: Yonghong Yao

Copyright © 2012 Cun-lin Li. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper deals with bimatrix games in uncertainty environment based on several types of ordering, which Maeda proposed. But Maeda’s models was just made based on symmetrical triangle fuzzy variable. In this paper, we generalized Maeda’s model to the non-symmetrical environment. In other words, we investigated the fuzzy bimatrix games based on nonsymmetrical 𝐿 - 𝑅 fuzzy variables. Then the pseudoinverse of a nonconstant monotone function was given and the concept of crisp parametric bimatrix games was introduced. At last, the existence condition of Nash equilibrium strategies of the fuzzy bimatrix games is proposed and (weak) Pareto equilibrium of the fuzzy bimatrix games was obtained through the Nash equilibrium of the crisp parametric bimatrix.