VISCOSITY SOLUTIONS FOR BILEVEL PROBLEMS WITH NASH EQUILIBRIUM CONSTRAINTS
A regularization method for bilevel problems with lower level defined by Nash equilibria is considered and a concept of “viscosity solution” associated to such a regularization is introduced. Sufficient conditions for the existence of viscosity solutions are given and applications to optimistic and pessimistic bilevel optimization problems are presented.
bilevel problem, Nash equilibrium, set-valued map, epiconvergence.
