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

Article Type

Research Article

Publication Title

International Game Theory Review

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.

DOI

https://10.1142/S0219198922500190

Publication Date

3-1-2023

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