Regularized Two-Stage Stochastic Variational Inequalities for Cournot-Nash Equilibrium Under Uncertainty (Journal of Computational Mathematics, 2021)
A convex two-stage non-cooperative multi-agent game under uncertainty is formulatedas a two-stage stochastic variational inequality (SVI). Under standard assumptions, weprovide sufficient conditions for the existence of solutions of the two-stage SVI and propose a regularized sample average approximation method for solving it. We prove theconvergence of the method as the regularization parameter tends to zero and the samplesize tends to infinity. Moreover, our approach is applied to a two-stage stochastic production and supply planning problem with homogeneous commodity in an oligopolisticmarket. Numerical results based on historical data in crude oil market are presented todemonstrate the effectiveness of the two-stage SVI in describing the market share of oilproducing agents.