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A Note on Linear Complementarity via Two-Person Zero-Sum Games

Author

Listed:
  • Dipti Dubey

    (Department of Mathematics, Shiv Nadar University, Dadri, UP 201314, India)

  • S. K. Neogy

    (Indian Statistical Institute, 7, S. J. S. Sansanwal Marg, New Delhi 110016, India)

  • T. E. S. Raghavan

    (Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, 851 S. Morgan, Chicago, IL 60607, USA)

Abstract

The matrix M of a linear complementarity problem can be viewed as a payoff matrix of a two-person zero-sum game. Lemke’s algorithm can be successfully applied to reach a complementary solution or infeasibility when the game satisfies the following conditions: (i) Value of M is equal to zero. (ii) For all principal minors of MT (transpose of M) value is non-negative. (iii) For any optimal mixed strategy y of the maximizer either yi > 0 or (My)i > 0 for each coordinate i.

Suggested Citation

  • Dipti Dubey & S. K. Neogy & T. E. S. Raghavan, 2023. "A Note on Linear Complementarity via Two-Person Zero-Sum Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 25(01), pages 1-8, March.
    • Handle: RePEc:wsi:igtrxx:v:25:y:2023:i:01:n:s0219198922500190
    DOI: 10.1142/S0219198922500190
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