Linear complementarity problems and bi-linear games

Gokulraj Sengodan; Chandrashekaran Arumugasamy

Applications of Mathematics (2020)

  • Volume: 65, Issue: 5, page 665-675
  • ISSN: 0862-7940

Abstract

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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 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.

How to cite

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Sengodan, Gokulraj, and Arumugasamy, Chandrashekaran. "Linear complementarity problems and bi-linear games." Applications of Mathematics 65.5 (2020): 665-675. <http://eudml.org/doc/296998>.

@article{Sengodan2020,
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 $\{\bf Z\}$-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.},
author = {Sengodan, Gokulraj, Arumugasamy, Chandrashekaran},
journal = {Applications of Mathematics},
keywords = {bimatrix game; nash equilibrium; $\{\bf Z\}$-transformation; semi positive map},
language = {eng},
number = {5},
pages = {665-675},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Linear complementarity problems and bi-linear games},
url = {http://eudml.org/doc/296998},
volume = {65},
year = {2020},
}

TY - JOUR
AU - Sengodan, Gokulraj
AU - Arumugasamy, Chandrashekaran
TI - Linear complementarity problems and bi-linear games
JO - Applications of Mathematics
PY - 2020
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 65
IS - 5
SP - 665
EP - 675
AB - 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.
LA - eng
KW - bimatrix game; nash equilibrium; ${\bf Z}$-transformation; semi positive map
UR - http://eudml.org/doc/296998
ER -

References

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