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In this paper, we first devise two algorithms to determine whether or not abimatrix game has a strategically equivalent zero-sum game. If so, we proposean algorithm that computes the strategically equivalent zero-sum game. If agiven bimatrix game is not strategically equivalent to a zero-sum game, we thenpropose an approach to compute a zero-sum game whose saddle-point equilibriumcan be mapped to a well-supported approximate Nash equilibrium of the originalgame. We conduct extensive numerical simulation to establish the efficacy ofthe two algorithms.

Two Algorithms for Computing Exact and Approximate Nash Equilibria in Bimatrix Games