Existence Results for Quasi-variational Inequalities with Applications to Radner Equilibrium Problems: Resolution Through Variational Inequalities

A quasi-variational inequality corresponds to a variational inequality in which the constraint set depends on the current value of the variable. Quasi-variational inequalities are known to be very useful for the modelling and analysis of many problems of economics and engineering, like generalized Nash equilibrium problems. Nevertheless, in the literature, there are only few existence results for those difficult problems. Our aim in this work is to identify a class of quasi-variational inequalities for which each solution of an auxiliary (classical) Stampacchia variational inequality provides a solution of the quasi-variational inequality. This class of quasi-variational inequalities is directly inspired by the Radner equilibrium problem, that is an equilibrium problem for economies involving sequential trade under conditions of uncertainty. By the way an existence result for Radner equilibrium problem with quasi-convex and possibly nonsmooth utility functions will be deduced.