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

Dipti Dubey (), S. K. Neogy () and T. E. S. Raghavan
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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

International Game Theory Review (IGTR), 2023, vol. 25, issue 01, 1-8

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.

Keywords: Linear complementarity problem; two-person zero-sum game; Lemke’s algorithm (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1142/S0219198922500190

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