The two-stage stochastic variational inequalities (SVIs) are able to characterize the optimality condition for the two-stage stochastic programming, and are very useful in real application problems. It can be applied to formulate the two-stage stochastic production and supply planning problem with homogeneous commodity in an oligopolistic market. In particular, we focus on explaining the market share in oil market by the two-stage SVIs. Numerical results based on historical data in crude oil market are presented to demonstrate the effectiveness of the two-stage SVIs in describing the market share of oil producing agents.