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We consider the problem of computing all Nash equilibria in bimatrix games (i.e., nonzero-sum two-player noncooperative games). Computing all Nash equilibria for large bimatrix games using single-processor computers is not feasible due to the exponential time required by the existing algorithms. We consider the use of parallel computing which allows us to solve larger games. We design and implement a parallel algorithm for computing all Nash Equilibria in bimatrix games. The algorithm computes all Nash equilibria by searching all possible supports of mixed strategies. We perform experiments on a cluster computing system to evaluate the performance of the parallel algorithm.