Robust Bayesian methods for Stackelberg security games

Recent work has applied game-theoretic models to real-world security problems at the Los Angeles International Airport (LAX) and Federal Air Marshals Service (FAMS). The analysis of these domains is based on input from domain experts intended to capture the best available intelligence information about potential terrorist activities and possible security countermeasures. Nevertheless, these models are subject to significant uncertainty---especially in security domains where intelligence about adversary capabilities and preferences is very difficult to gather. This uncertainty presents significant challenges for applying game-theoretic analysis in these domains. Our experimental results show that standard solution methods based on perfect information assumptions are very sensitive to payoff uncertainty, resulting in low payoffs for the defender. We describe a model of Bayesian Stackelberg games that allows for general distributional uncertainty over the attacker's payoffs. We conduct an experimental analysis of two algorithms for approximating equilibria of these games, and show that the resulting solutions give much better results than the standard approach when there is payoff uncertainty.