Bimatrix Equilibrium Points and Mathematical Programming

Abstract

Some simple constructive proofs are given of solutions to the matric system Mz − ω = q; z ≧ 0; ω ≧ 0; and z T ω = 0, for various kinds of data M, q, which embrace the quadratic programming problem and the problem of finding equilibrium points of bimatrix games. The general scheme is, assuming non-degeneracy, to generate an adjacent extreme point path leading to a solution. The scheme does not require that some functional be reduced.