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Keywords:
bimatrix game; nash equilibrium; ${\bf Z}$-transformation; semi positive map
Summary:
In this paper, we define bi-linear games as a generalization of the bimatrix games. In particular, we generalize concepts like the value and equilibrium of a bimatrix game to the general linear transformations defined on a finite dimensional space. For a special type of ${\bf Z}$-transformation we observe relationship between the values of the linear and bi-linear games. Using this relationship, we prove some known classical results in the theory of linear complementarity problems for this type of ${\bf Z}$-transformations.
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