  We study nested variational inequalities, which are variational inequalities
whose feasible set is the solution set of another variational inequality. We
present a projected averaging Tikhonov algorithm requiring the weakest
conditions in the literature to guarantee the convergence to solutions of the
nested variational inequality. Specifically, we only need monotonicity of the
upper- and the lower-level variational inequalities. Also, we provide the first
complexity analysis for nested variational inequalities considering optimality
of both the upper- and lower-level.
