Mixed complementarity problems for robust optimization equilibrium in bimatrix game

Guimei Luo

Applications of Mathematics (2012)

  • Volume: 57, Issue: 5, page 503-520
  • ISSN: 0862-7940

Abstract

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In this paper, we investigate the bimatrix game using the robust optimization approach, in which each player may neither exactly estimate his opponent’s strategies nor evaluate his own cost matrix accurately while he may estimate a bounded uncertain set. We obtain computationally tractable robust formulations which turn to be linear programming problems and then solving a robust optimization equilibrium can be converted to solving a mixed complementarity problem under the l 1 ∩ l ∞ -norm. Some numerical results are presented to illustrate the behavior of the robust optimization equilibrium.

How to cite

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Luo, Guimei. "Mixed complementarity problems for robust optimization equilibrium in bimatrix game." Applications of Mathematics 57.5 (2012): 503-520. <http://eudml.org/doc/246628>.

@article{Luo2012,
abstract = {In this paper, we investigate the bimatrix game using the robust optimization approach, in which each player may neither exactly estimate his opponent’s strategies nor evaluate his own cost matrix accurately while he may estimate a bounded uncertain set. We obtain computationally tractable robust formulations which turn to be linear programming problems and then solving a robust optimization equilibrium can be converted to solving a mixed complementarity problem under the $l_1\cap l_\infty $-norm. Some numerical results are presented to illustrate the behavior of the robust optimization equilibrium.},
author = {Luo, Guimei},
journal = {Applications of Mathematics},
keywords = {robust optimization equilibrium; bimatrix game; $l_1\cap l_\infty $-norm; mixed complementarity problem; robust optimization equilibrium; bimatrix game; -norm; mixed complementarity problem},
language = {eng},
number = {5},
pages = {503-520},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Mixed complementarity problems for robust optimization equilibrium in bimatrix game},
url = {http://eudml.org/doc/246628},
volume = {57},
year = {2012},
}

TY - JOUR
AU - Luo, Guimei
TI - Mixed complementarity problems for robust optimization equilibrium in bimatrix game
JO - Applications of Mathematics
PY - 2012
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 57
IS - 5
SP - 503
EP - 520
AB - In this paper, we investigate the bimatrix game using the robust optimization approach, in which each player may neither exactly estimate his opponent’s strategies nor evaluate his own cost matrix accurately while he may estimate a bounded uncertain set. We obtain computationally tractable robust formulations which turn to be linear programming problems and then solving a robust optimization equilibrium can be converted to solving a mixed complementarity problem under the $l_1\cap l_\infty $-norm. Some numerical results are presented to illustrate the behavior of the robust optimization equilibrium.
LA - eng
KW - robust optimization equilibrium; bimatrix game; $l_1\cap l_\infty $-norm; mixed complementarity problem; robust optimization equilibrium; bimatrix game; -norm; mixed complementarity problem
UR - http://eudml.org/doc/246628
ER -

References

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