Quasi-variational inequalities on product spaces and its applications to stochastic equilibrium problems
Shivani Valecha, Asrifa Sultana · Optimization · 2025
We study a class of quasi-variational inequalities defined on the product of Banach spaces. An operator formed by the product of generalized monotone and locally upper sign-continuous operators need not preserve the same properties. Under these assumptions on the component operators, we ensure the solutions to the proposed product-type quasi-variational inequalities by applying a preliminary existence result on variational inequalities. As an application, we study the multi-stage stochastic economic equilibrium problems, in which uncertainty is characterized by an uncountable set of scenarios at each stage and the expected utility functions of agents are quasiconcave.