Regularized Two-Stage Stochastic Variational Inequalities for Cournot-Nash Equilibrium Under Uncertainty

Jie Jiang, Yun Shi, Xiaozhou Wang, Xiaojun Chen

Research output: Journal article publicationJournal articleAcademic researchpeer-review


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.
Original languageEnglish
Pages (from-to)813-842
Number of pages29
JournalJournal of Computational Mathematics
Issue number6
Publication statusPublished - 20 Nov 2019


  • Two-stage stochastic variational inequalities
  • Regularized method
  • Progressive hedging method
  • Uncertainty
  • Oil market share


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