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Volume 37, Issue 6
Regularized Two-Stage Stochastic Variational Inequalities for Cournot-Nash Equilibrium Under Uncertainty

Jie Jiang, Yun Shi, Xiaozhou Wang & Xiaojun Chen

DOI: 10.4208/jcm.1906-m2019-0025

J. Comp. Math., 37 (2019), pp. 813-842.

Published online: 2019-11

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  • Abstract

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.

  • Keywords

Two-stage stochastic variational inequalities, Cournot-Nash equilibrium, Regularized method, Progressive hedging method, Uncertainty, Oil market share.

  • AMS Subject Headings

90C15, 90C33

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

jie.jiang@connect.polyu.hk (Jie Jiang)

yun.shi@connect.polyu.hk (Yun Shi)

xzhou.wang@connect.polyu.hk (Xiaozhou Wang)

xiaojun.chen@polyu.edu.hk (Xiaojun Chen)

  • BibTex
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  • TXT
@Article{JCM-37-813, author = {Jiang , JieShi , YunWang , Xiaozhou and Chen , Xiaojun}, 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 = {

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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1906-m2019-0025}, url = {http://global-sci.org/intro/article_detail/jcm/13376.html} }
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 -

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.

Jie Jiang, Yun Shi, Xiaozhou Wang & Xiaojun Chen. (2019). Regularized Two-Stage Stochastic Variational Inequalities for Cournot-Nash Equilibrium Under Uncertainty. Journal of Computational Mathematics. 37 (6). 813-842. doi:10.4208/jcm.1906-m2019-0025
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