Branch-and-price with novel cuts, and a new Stackelberg Security Game

TL;DR

This paper introduces a branch-and-price method with novel valid inequalities to efficiently compute Strong Stackelberg Equilibria in security games, improving upon existing formulations and demonstrating superior computational performance.

Contribution

The paper presents a new branch-and-price approach with innovative cuts for solving Stackelberg security games more effectively than standard methods.

Findings

Outperforms standard formulations in computational experiments.

Novel valid inequalities improve solution quality and speed.

Performance varies with different game parameters and settings.

Abstract

Anticipating the strategies of potential attackers is crucial for protecting critical infrastructure. We can represent the challenge of the defenders of such infrastructure as a Stackelberg security game. The defender must decide how to allocate limited resources to protect specific targets, aiming to maximize their expected utility (such as minimizing the extent of damage) and considering that attackers will respond in a way that is most advantageous to them. We present novel valid inequalities to find a Strong Stackelberg Equilibrium in both Stackelberg games and Stackelberg security games. We also consider a Stackelberg security game that aims to protect targets with a defined budget. We use branch-and-price in this game to show that our approach outperforms the standard formulation in the literature, and we conduct an extensive computational study to analyze the impact of various branch-and-price parameters on the performance of our method in different game settings.