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

Bin Zhou; Hailin Sun

doi:10.3934/naco.2020049

Article Contents

2020, Volume 10, Issue 4: 521-535. Doi: 10.3934/naco.2020049

This issue Previous Article Parameter-related projection-based iterative algorithm for a kind of generalized positive semidefinite least squares problem Next Article Survey of derivative-free optimization

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

Bin Zhou and
Hailin Sun^,

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

^* Corresponding author: Hailin Sun
^* Corresponding author: Hailin Sun

Received: April 2020

Revised: September 2020

Published online: December 2020

The work is supported by NSFC grant 11871276.

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Abstract

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.

Keywords:

Two-stage stochastic variational inequalities,
stochastic game,
risk averse,
smoothing,
regularization.

Mathematics Subject Classification: Primary: 90C15; Secondary: 90C33.

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