Solving a Matrix Game by Linear Programming

This paper presents (1) a new characterization, via linear programming, of extreme optimal strategies of a matrix game and (2) a simple direct procedure for computing them. The first pertains to the neat formulas of L. S. Shapley and R. N. Snow for a “basic solution”, and the second to the highly effective “simplex method” of G. B. Dantzig. Both are related to the author's “combinational equivalence” of matrices, the first through an optimal block-pivot transformation and the second through a suitably chosen succession of elementary pivot steps.