# American Institute of Mathematical Sciences

December  2020, 10(4): 521-535. doi: 10.3934/naco.2020049

## Two-stage stochastic variational inequalities for Cournot-Nash equilibrium with risk-averse players under uncertainty

 Jiangsu Provincial Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing, 210023, China

* Corresponding author: Hailin Sun

Received  April 2020 Revised  September 2020 Published  September 2020

Fund Project: The work is supported by NSFC grant 11871276

A convex two-stage non-cooperative game with risk-averse players under uncertainty is formulated as a two-stage stochastic variational inequality (SVI) for point-to-set operators. Due to the indifferentiability of function $(\cdot)_+$ and the discontinuity of solution mapping of the second-stage problem, under standard assumptions, we propose a smoothing and regularization method to approximate it as a two-stage SVI in point-to-point case with continuous second stage solution functions. The corresponding convergence analysis is also given.

Citation: Bin Zhou, Hailin Sun. Two-stage stochastic variational inequalities for Cournot-Nash equilibrium with risk-averse players under uncertainty. Numerical Algebra, Control & Optimization, 2020, 10 (4) : 521-535. doi: 10.3934/naco.2020049
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