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      https://www.ias.ac.in/article/fulltext/pmsc/130/0047

    • Keywords

       

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

    • Abstract

       

      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.

    • Author Affiliations

       

      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
    • Dates

       
  • Proceedings – Mathematical Sciences | News

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