Two-Stage Stochastic Variational Inequalities For Nash Equilibrium With Risk-Averse Players Under Uncertainty

This paper studies the process of non-cooperative games by making two-stage decisions in a random market environment to achieve equilibrium.Compared with single-stage decision-making,two-stage decision-making can make better use of future information.Therefore,in today's increasingly fierce competition,producers are more inclined to adopt two-stage decision-making to avoid risks,which makes the two-stage stochastic non-cooperative game between multiple manufacturers become significant in the random environment.A convex two-stage non-cooperative game with risk-averse players under uncertainty is formulated as a two-stage stochastic variational inequality(SVI)for pointto-set operators.Due to the indifferentiability of function(·)+ 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.Furthermore,the two-stage stochastic nonlinear complementarity problem(SNCPS)is considered.We reduce the conditions in reference[8]that the second-stage function is continuously differentiale to the requirement that the second-stage function is Lipschitz continuous.Under these weaker conditions,the strong monotony holds true.