A convex two-stage non-cooperative multi-agent game under uncertainty is formulated as a two-stage stochastic variational inequality (SVI). Under standard assumption, 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, we apply our approach to a two-stage stochastic production and supply planning game with homogeneous commodity in an oligopolistic market. Numerical results based on historical data in crude oil market are presented to show the effectiveness of the two-stage SVI for describing the market share of oil producing agents in the last half a century.