Quasi-variational equation

The main result proved in this article is the following. There is an (x) over bar is an element of X such that g((x) over bar) is an element of C((x) over bar) and sup (yis an element ofC((x) over bar)) Psi((x) over bar, y) = Psi((x) over bar, g((x) over bar)) where C : X --> 2(Y) is a correspondence; (g is a function defined over X in Y) and a function Psi defined over X x Y in R; X and Y are different sets. This results generalizes the quasi-variational inequation. According to this result, we show the existence of generalized Berge strong equilibrium for a constrained non cooperative game.