Abstract
We consider a class of stochastic Nash equilibrium problems (SNEP). Under some mild conditions, we reformulate the SNEP as a stochastic mixed complementarity problem (SMCP). We apply the well-known sample average approximation (SAA) method to solve the SMCP. We further introduce a semismooth Newton method to solve the SAA problems. The comprehensive convergence analysis is given as well. In addition, we demonstrate the proposed approach on a stochastic Nash equilibrium model in the wholesale gas–oil markets.
Acknowledgements
The authors are grateful to the two anonymous referees for their helpful comments and suggestions. This paper was presented at The Eighth International Conference on Optimization: Techniques and Applications (ICOTA8) in Shanghai, December 2010. This work was supported in part by NSFC Grant #11071028.