Sampling average approximation method for a class of stochastic Nash equilibrium problems

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.

Keywords:

• stochastic Nash equilibrium problem
• sample average approximation method
• semismooth Newton method

2010 Mathematics Subject Classification:

• 65H10
• 65K10
• 90C15
• 90C33

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.

Additional information

Notes on contributors

Gui-Hua Lin

Current address: School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, People's Republic of China.