This paper presents an algorithm for calculating mixed Nash equilibria in 2-player games. The algorithm is based on the mathematical equivalence between the expected payoff function of bi-matrix games and the fuzzy average. It was proved that the expected payoff function of 2-player games is identical to the fuzzy average of two linguistic values when the payoff matrix is replaced with the consequence matrix, the strategy sets are replaced with term sets in linguistic variables. This paper proves that the new algorithm can compute mixed NE in 2-player games within polynomial time for any types of bi-matrix games. We claim that there is a fully polynomial time scheme for computing mixed NE in 2-player games.
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