On the exact solution of a class of Stackelberg games

This paper presents a mixed-integer linear reformulation for a subclass of two-level nonlinear discrete-continuous decision problems also known as Stackelberg strategic games. Solving the original (two-level and nonlinear) model is algorithmically challenging. In fact, even global solvers for standard (or single-level) mixed-integer nonlinear programs are difficult to implement and relatively inaccessible. The proposed transformation allows solving this class of Stackelberg games using mixed-integer linear programming theory for which optimized solvers with large-scale computational capabilities have been reported. Furthermore, the proposed reformulation is achieved without adding any new integer variables to the original model, a desired computational property in case a large portion of the search tree has to be enumerated.