Iteration in a subspace for solving matrix games

A new method for solving symmetric matrix games is proposed and justified. It is based on iterating vectors in the null space of a specially constructed matrix. According to the numerical tests performed, the efficiency of the proposed method is comparable with that of the available iterative algorithms having about the same computational complexity. This approach is also applicable to more complicated problems than the calculation of particular optimal strategies. For instance, it can be used for finding the unique minimum length solution.