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Bimatrix Equilibrium Points and Mathematical Programming

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  • C. E. Lemke

    (Rensselaer Polytechnic Institute, Troy, New York)

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.

Suggested Citation

  • C. E. Lemke, 1965. "Bimatrix Equilibrium Points and Mathematical Programming," Management Science, INFORMS, vol. 11(7), pages 681-689, May.
    • Handle: RePEc:inm:ormnsc:v:11:y:1965:i:7:p:681-689
    DOI: 10.1287/mnsc.11.7.681
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