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.
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: email@example.com, firstname.lastname@example.org