@Article{JCM-37-6,
author = {Jie, Jiang and Yun, Shi and Xiaozhou, Wang and Xiaojun, Chen},
title = {Regularized Two-Stage Stochastic Variational Inequalities for Cournot-Nash Equilibrium Under Uncertainty},
journal = {Journal of Computational Mathematics},
year = {2019},
volume = {37},
number = {6},
pages = {813--842},
abstract = {<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>},
issn = {1991-7139},
doi = {https://doi.org/10.4208/jcm.1906-m2019-0025},
url = {https://global-sci.com/article/84448/regularized-two-stage-stochastic-variational-inequalities-for-cournot-nash-equilibrium-under-uncertainty}
}