TY - JOUR
T1 - Regularized Two-Stage Stochastic Variational Inequalities for Cournot-Nash Equilibrium Under Uncertainty
AU - Jiang , Jie
AU - Shi , Yun
AU - Wang , Xiaozhou
AU - Chen , Xiaojun
JO - Journal of Computational Mathematics
VL - 6
SP - 813
EP - 842
PY - 2019
DA - 2019/11
SN - 37
DO - http://doi.org/10.4208/jcm.1906-m2019-0025
UR - https://global-sci.org/intro/article_detail/jcm/13376.html
KW - Two-stage stochastic variational inequalities, Cournot-Nash equilibrium, Regularized method, Progressive hedging method, Uncertainty, Oil market share.
AB - <p style="text-align: justify;">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.</p>