A branch and price algorithm for a Stackelberg Security Game

Abstract

Mixed integer optimization formulations are an attractive alternative to solve Stackelberg Game problems thanks to the efficiency of state of the art mixed integer algorithms. In particular, decomposition algorithms, such as branch and price methods, make it possible to tackle instances large enough to represent games inspired in real world domians.

In this work we focus on Stackelberg Games that arise from a security application and investigate the use of a new branch and price method to solve its mixed integer optimization formulation. We prove that the algorithm provides upper and lower bounds on the optimal solution at every iteration and investigate the use of stabilization heuristics. Our preliminary computational results compare this solution approach with previous decomposition methods obtained from alternative integer programming formulations of Stackelberg games.