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Bilevel programs with spatial price equilibrium constraints are strategicmodels that consider a price competition at the lower-level. These models findapplication in facility location-price models, optimal bidding in powernetworks, and integration of renewable energy sources in distribution networks.In this paper, for the case where the equilibrium at the lower level can beformulated as an optimization problem, we introduce an enhanced single-levelformulation based on duality and show that its relaxation is stronger than theusual single-level formulation obtained using KKT conditions. Compared to theliterature [1, 2], this new formulation is (i) computationally friendly toglobal solution strategies using branch-and-bound, and (ii) able to handlelarger instance sizes. Further, we develop a heuristic procedure to findfeasible solutions inside of the branch-and-bound tree that is effective onlarge-sized instances and produces solutions whose objective values are closeto the relaxation bound. We demonstrate the benefits of this formulation andheuristic through an extensive numerical study on synthetic instances ofEquilibrium Facility Location [3] and on standard IEEE bus networks forplanning renewable generation capacity under uncertainty.

Globally Solving a Class of Bilevel Programs with Spatial Price Equilibrium Constraints