Geodesic
Linear complementarity problems and bi-linear games
Applications of Mathematics, Tome 65 (2020) no. 5, pp. 665-675.

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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.
DOI : 10.21136/AM.2020.0371-19
Classification : 15A63, 90C33, 91A05
Keywords: bimatrix game; nash equilibrium; ${\bf Z}$-transformation; semi positive map 
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Sengodan, Gokulraj; Arumugasamy, Chandrashekaran. Linear complementarity problems and bi-linear games. Applications of Mathematics, Tome 65 (2020) no. 5, pp. 665-675. doi : 10.21136/AM.2020.0371-19. http://geodesic.mathdoc.fr/articles/10.21136/AM.2020.0371-19/

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