  A convex two-stage non-cooperative multi-agent game under uncertainty is
formulated as a two-stage stochastic variational inequality (SVI). Under
standard assumptions, we provide 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 the convergence of the method as
the regularization parameter tends to zero and the sample size tends to
infinity. Moreover, our approach is applied to a two-stage stochastic
production and supply planning problem with homogeneous commodity in an
oligopolistic market. Numerical results based on historical data in crude oil
market are presented to demonstrate the effectiveness of the two-stage SVI in
describing the market share of oil producing agents.
