Solution behaviour for parameter-dependent quasi-variational inequalities

In this paper the solution behaviour of a class of parameter-dependent quasi-variational inequalities is analysed. By using sensitivity and stability results for monotone variational inequalities and the Implicit Function Theorem of F.H. Clarke, the paper derives conditions under which the perturbed solution of a parametric quasi-variational inequality is locally unique, lipschitzian and directionally differentiable. These results are particularized in the case of parametric implicit complementary problems.