Factorization of quasi-variational relations systems

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.