Strategic Security Placement in Network Domains with Applications to Transit Security

Deterministic placement of security personnel creates serious vulnerabilities for any organization attempting to prevent intrusion. Recent work in use at the Los Angeles International Airport (LAX) and in progress with the United States Federal Air Marshal Service (FAMS) has applied game-theoretic analysis to the problem by modeling it as a Stackelberg game wherein security forces are the leaders that commit to a strategy that is observed and countered by attackers. In this work, we explore efficient techniques for performing the same analysis on games with a graph structure, wherein an attacker must follow a path from an entry point to a target. If we frame these problems in the straightforward manner with leader actions being sets of edges that can be guarded and follower actions being paths from entry to targets, the size of the game increases exponentially, quickly reaching memory limitations when using general Stackelberg solvers. In this work, we propose a novel linear program that is able to solve this type of problem efficiently. While it provides exact solutions for games where only one checkpoint is allowed, it is an approximation in the general case. Finally, we compare the performance of this and other methods by generating optimal policies for the Seoul Metropolitan Subway in Seoul, South Korea.