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Zero sum matrix games; bimatrix games; skew symmetric matrices; completely mixed bimatrix games.

Kaplansky (Ann. Math. 46(3) (1945) 474–479) introduced the notion of completely mixed games. Fifty years later in 1995, he wrote another beautiful paper where he gave a set of necessary and sufficient conditions for a skew symmetric matrix game to be completely mixed. In this work, we attempt to answer when bimatrix games will be completely mixed. In particular, we give a set of necessary and sufficient condition for a bimatrix game $(A, B)$ to be completely mixed when $A$ and $B$ are skew symmetric matrices of order 3. We give several examples to show the sharpness of our result. We also formulate a conjecture when $A$ and $B$ are skew symmetric matrices of order 5.

T Parthasarathty¹ Vasudha Sharma² A R Sricharan²

1. Indian Statistical Institute, Chennai Centre, 37 Nelson Manickam Road, Chennai 600 029, India
2. Chennai Mathematical Institute, Siruseri, Kelambakkam, Chennai 603 103, India

Published

25 July 2020

Final version published online

25 July 2020