  Bilevel programs with spatial price equilibrium constraints are strategic
models that consider a price competition at the lower level. These models find
application in facility location-price models, optimal bidding in power
networks, and integration of renewable energy sources in distribution networks.
In this paper, for the case where the equilibrium at the lower level can be
formulated as an optimization problem, we introduce an enhanced single-level
formulation based on duality and show that its relaxation is stronger than the
single-level formulation obtained using KKT conditions. Compared to the
literature [1, 2], this new formulation (i) is computationally friendly to
global solution strategies using branch-and-bound, and (ii) can tackle
instances of larger size. Further, we develop a heuristic procedure to find
feasible solutions inside of the branch-and-bound tree that is effective on
instances of large size and produces solutions whose objective values are close
to the relaxation bound. We demonstrate the benefits of this formulation and
heuristic through an extensive numerical study on synthetic instances of
Equilibrium Facility Location [3] and on standard IEEE bus networks for
planning renewable generation capacity under uncertainty.
