  We introduce new types of systems of generalized quasi-variational
inequalities and we prove the existence of the solutions by using results of
pair equilibrium existence for free abstract economies. We consider the fuzzy
models and we also introduce the random free abstract economy and the random
equilibrium pair. The existence of the solutions for the systems of
quasi-variational inequalities comes as consequences of the existence of
equilibrium pairs for the considered free abstract economies.

Optimization and Control