Factorization of quasi-variational relations systems

TL;DR

This paper investigates the conditions under which solutions to individual quasi-variational relation problems imply solutions to the entire system, with applications to variational inequalities and Nash equilibrium problems.

Contribution

It establishes new conditions linking the solvability of independent problems to the existence of solutions for the coupled system.

Findings

Conditions for solvability of the system derived

Application to variational inequalities demonstrated

Application to constrained Nash equilibrium provided

Abstract

Variational relation problems allow a general approach for variational inequalities, equilibrium problems, optimization problems, variational inclusions. In this paper we consider a system of quasi-variational relations and determine some conditions in which the solvability of the independent problems imply the existence of a solution for the system. We particularize then the result for a system of variational inequalities and for a constrained Nash equilibrium problem.