Existence and Approximation Results Involving Regularized Constrained Stackelberg Problems

We are concerned with two-level optimization problems, corresponding to nonzero-sum noncooperative games, in which the set of optimal solutions to the lower level problem is not a singleton. We are interested in Stackelberg solutions first introduced by H. Von Stackelberg in the context of economic competition. Our aim is to extend some approximation and existence results given by Loridan and Morgan by considering the case when the set of constraints in the upper level problem depends on the set of optimal solutions to the lower level problem.