Sample average approximation method for a class of stochastic generalized Nash equilibrium problems

We consider a class of stochastic generalized Nash equilibrium problems (SGNEPs). Under some mild conditions, we reformulate the SGNEP as a stochastic mixed complementarity problem (SMCP). We apply the well-known sample average approximation (SAA) method to solve the SMCP. We further introduce an interior point method to solve the SAA problems. Comprehensive convergence analysis is given as well. In addition, we demonstrate the proposed approach on a stochastic generalized Nash equilibrium model in river basin pollution game.