Inspired by the progressive decoupling of linkages methodology for optimization and
variational inequalities, we propose an algorithm for solving quasi-variational inequalities
as a sequence of variational inequalities. Our method is shown to converge locally under
some regularity conditions and globally when such conditions hold throughout the entire
domain. Separately, under other type of assumptions, global convergence with linear rate
is also established for the class of quasi-variational inequalities said to have a moving set.
Advantageous computational performance is shown for large-scale Walrasian equilibrium
problems, a special case of generalized Nash equilibria, as well as for some other instances
encountered in related literature.