An algorithm for finding approximate Nash equilibria in bimatrix games

Abstract

This paper describes an algorithm for calculating approximately mixed Nash equilibria (NE) in bimatrix games. The algorithm fuzzifies the strategies with normalized possibility distributions. The fuzzification takes advantage of the piecewise linearity of possibility distributions and transforms the NE problem of bimatrix games into a reduced form. The algorithm is guaranteed to find approximate NE in bimatrix games and ensures that the approximate NE is the saddle point of expected payoff functions in the reduced form. The algorithm provides a method of determining how close an approximate NE is to a solution during computation. Numerical results show that the new algorithm is approximately seven-time faster than the Lemke–Howson (LH) algorithm when the game size is 96, and the value of approximation deviation can be as small as 0.1.