In this paper, the necessary and sucient condition for the existence anduniqueness of a completely mixed Nash equilibrium in bimatrix games [A;AT ] are pre-sented. Matrix A 2 Rnn is a payo matrix. The necessary and sucient condition areexpressed with some properties of saddle point matrices, denoted by (A; e), where e isthe column vector with all entries 1. Properties of the saddle point matrices assessedusing the algebraic approach.
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