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This paper presents a parallel randomized algorithm which computes a pair of @e-optimal strategies for a given (m,n)-matrix game A = [a"i"j] @e [-1, 1] in O(@e^-^2log^2(n+m)) expected time on an (n+m)/log(n+m)-processor EREW PRAM. For any fixed accuracy @e 0, the expected sequential running time of the suggested algorithm is O((n + m)log(n + m)), which is sublinear in mn, the number of input elements of A. On the other hand, simple arguments are given to show that for @e