Addressing uncertainty in stackelberg games for security: models and algorithms

Recently, there has been significant research interest in using game-theoretic approaches to allocate limited security resources to protect physical infrastructure including ports, airports, transit systems, and other critical national infrastructure as well as natural resources such as forests, tigers, fish, and so on. Indeed, the leader-follower Stackelberg game model is at the heart of many deployed applications. In these applications, the game model provides a randomized strategy for the leader (security forces), under the assumption that the adversary will conduct surveillance before launching an attack. Inevitably, the security forces are faced with the problem of uncertainty. For example, a security officer may execute a patrol strategy differently from the planned one due to unexpected events. Also the adversaries may have different types in terms of their preferences, objectives, and capabilities. While Bayesian Stackelberg games for modeling discrete uncertainty have been successfully used in deployed applications, they are NP-hard problems and existing methods perform poorly in scaling up the number of types: inadequate for complex real world problems. Furthermore, Bayesian Stackelberg games have not been applied to model execution and observation uncertainty and finally, they require the availability of full distributional information of the uncertainty. To overcome these difficulties, my thesis presents four major contributions. First, I provide a novel algorithm HUNTER for Bayesian Stackelberg games to scale up the number of types. Exploiting the efficiency of H UNTER, I show preference, execution and observation uncertainty can be addressed in a unified framework. Second, addressing execution and observation uncertainty whose distribution is difficult to estimate, I provide a robust optimization formulation to compute the optimal risk-averse leader strategy for security problems motivated by the \ARMOR application. Third, addressing the uncertainty of the adversary's capability of conducting surveillance, I show that for a class of Stackelberg games motivated by real security applications, the leader is always best-responding with a Stackelberg equilibrium strategy regardless of whether the adversary conducts surveillance or not. As the final contribution, I provide TRUSTS, a novel game-theoretic formulation for scheduling randomized patrols in public transit domains where timing is a crucial component. TRUSTS addresses dynamic execution uncertainty in such spatiotemporal domains by integrating Markov Decision Processes into the game-theoretic model. Simulation results as well as real-world trials of TRUSTS in the Los Angeles Metro Rail system provide validations of the approach.