Interactions Between Bilevel Optimization and Nash Games
We aim at building a bridge between bilevel programming and generalized Nash equilibrium problems. First, we present two Nash games that turn out to be linked to the (approximated) optimistic version of the bilevel problem. Specifically, on the one hand we establish relations between the equilibrium set of a Nash game and global optima of the (approximated) optimistic bilevel problem. On the other hand, correspondences between equilibria of another Nash game and stationary points of the (approximated) optimistic bilevel problem are obtained.