Mixed complementarity problems for robust optimization equilibrium in bimatrix game

summary: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