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 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 Z -transformations.

中文翻译：

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线性互补问题和双线性博弈

在本文中，我们将双线性博弈定义为双矩阵博弈的泛化。特别是，我们将双矩阵博弈的值和均衡等概念推广到有限维空间上定义的一般线性变换。对于特殊类型的 Z 变换，我们观察线性和双线性博弈的值之间的关系。使用这种关系，我们证明了此类 Z 变换的线性互补问题理论中的一些已知经典结果。