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Robust optimization with applications to game theory

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Abstract:

In this article, we investigate robust optimization equilibria with two players, in which each player can neither evaluate his opponent's strategy nor his own cost matrix accurately while may estimate a bounded set of the strategy or cost matrix. We obtain a result that solving this equilibria can be formulated as solving a second-order cone complementarity problem under an ellipsoid uncertainty set or a mixed complementarity problem under a box uncertainty set. We present some numerical results to illustrate the behaviour of robust optimization equilibria.

Keywords: bimatrix game; cost matrix uncertainty; mixed complementarity problem; robust optimization equilibria; second-order cone complementarity problem; strategy uncertainty

Document Type: Research Article

DOI: http://dx.doi.org/10.1080/00036810903157196

Affiliations: 1: College of Mathematics and Econometrics, Hunan University, Changsha, Hunan 410082, PRC,Department of Mathematics, Guangdong University of Finance, Guangzhou, Guangdong 510521, PRC 2: College of Mathematics and Econometrics, Hunan University, Changsha, Hunan 410082, PRC 3: Department of Mathematics, Guangdong University of Finance, Guangzhou, Guangdong 510521, PRC

Publication date: August 1, 2009

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