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

Regularized Two-Stage Stochastic Variational Inequalities for Cournot-Nash Equilibrium Under Uncertainty
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Year:    2019

Author:    Jie Jiang, Yun Shi, Xiaozhou Wang, Xiaojun Chen

Journal of Computational Mathematics, Vol. 37 (2019), Iss. 6 : pp. 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jcm.1906-m2019-0025

Journal of Computational Mathematics, Vol. 37 (2019), Iss. 6 : pp. 813–842

Published online:    2019-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    30

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

Author Details

Jie Jiang

Yun Shi

Xiaozhou Wang

Xiaojun Chen

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