  We study connections between optimistic bilevel programming problems and
Generalized Nash Equilibrium Problems (GNEP)s. We remark that, when addressing
bilevel problems, we consider the general case in which the lower level program
is not assumed to have a unique solution. Inspired by the optimal value
approach, we propose a new GNEP model that is closely related to the bilevel
program. We provide a complete analysis of the relationship between the
"vertical" bilevel problem and the corresponding "horizontal" (one-level) GNEP
model. We define classes of problems for which solutions of the bilevel program
can be computed by finding equilibria of the GNEP. We develop a simple
algorithm, which turns out to be globally convergent, for the solution of
classes of our GNEP; we study how it is then possible to recover a solution of
the bilevel problem from the computed equilibrium. Numerical experience shows
the effectiveness of our approach, even when addressing big nonlinear bilevel
problems.
