A new method for solving Bimatrix game using LCP under fuzzy environment

Abstract

In this paper a new method is proposed for solving the Fully Fuzzy Bimatrix Game (FFBG) using Linear Complementarity approach. In FFBG the player’s payoff matrix is represented by trapezoidal fuzzy numbers. The given Fully Fuzzy Bimatrix Game is transformed into the Fully Fuzzy Linear Complementarity Problem (FLCP). Hence the FLCP with trapezoidal fuzzy number is converted into the FLCP with interval number using α - cut. Then we solve the Fuzzy Linear Complementarity Problem with interval numbers. The obtained solution of this FLCP is the solution of the given fuzzy Bimatrix Game. The effectiveness of the proposed method is illustrated by means of a numerical example.