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. © 2022 World Scientific Publishing Company.