Bimatrix Equilibrium Points and Mathematical Programming

C. E. Lemke
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C. E. Lemke: Rensselaer Polytechnic Institute, Troy, New York

Management Science, 1965, vol. 11, issue 7, 681-689

Abstract: Some simple constructive proofs are given of solutions to the matric system Mz - \omega - q; z \geqq 0; \omega \geqq 0; and z T \omega - 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.

Date: 1965
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