- - - Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran
- - - Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran
- - - Department of Mathematics and Computer Sciences, Amirkabir University of Technology, Tehran, Iran

In this paper, bi-matrix games are investigated based on L-R fuzzy variables. Also, based on the fuzzy max order several models in non-symmetrical L-R fuzzy environment is constructed and the existence condition of Nash equilibrium strategies of the fuzzy bi-matrix games is proposed. At last, based on the Nash equilibrium of crisp parametric bi-matrix games, we obtain the Pareto and weak Pareto Nash equilibrium strategies of the fuzzy bi-matrix games.

Bi-matrix game, Nash equilibrium, L-R fuzzy variable