Applications of Mathematics, Vol. 65, No. 5, pp. 665-675, 2020


Linear complementarity problems and bi-linear games

Gokulraj Sengodan, Chandrashekaran Arumugasamy

Received December 26, 2019.   Published online June 25, 2020.

Abstract:  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.
Keywords:  bimatrix game; nash equilibrium; $Z$-transformation; semi positive map
Classification MSC:  91A05, 90C33, 15A63
DOI:  10.21136/AM.2020.0371-19

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Affiliations:   Gokulraj Sengodan (corresponding author), Chandrashekaran Arumugasamy, Department of Mathematics, Central University of Tamil Nadu, Neelakudi Campus, Thiruvarur, Tamil Nadu, 610 005, India, e-mail: gokulrajs93@gmail.com, chandru1782@gmail.com


 
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