|edoc-Server der Humboldt-Universität zu Berlin|
Huifu Xu, University of Southampton|
Dali Zhang, University of Southampton
|Title:||Stochastic Nash Equilibrium Problems: Sample Average Approximation and Applications|
|Date of Acceptance:||19.12.2008|
Stochastic Programming E-Print Series |
|Editors:||Julie L. Higle; Werner Römisch; Surrajeet Sen|
|Complete Preprint:||pdf (urn:nbn:de:kobv:11-10094922)|
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|This paper presents a Nash equilibrium model where the underlying objective functions involve uncertainties and nonsmoothness. The well known sample average approximation method is applied to solve the problem and the ﬁrst order equilibrium conditions are characterized in terms of Clarke generalized gradients. Under some moderate conditions, it is shown that with probability one, a statistical estimator obtained from sample average approximate equilibrium problem converges to its true counterpart. Moreover, under some calmness conditions of the generalized gradients and metric regularity of the set-valued mappings which characterize the ﬁrst order equilibrium conditions, it is shown that with probability approaching one exponentially fast with the increase of sample size, the statistical estimator converge to its true counterparts. Finally, the model is applied to an equilibrium problem in electricity market.|
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