Game-theoretic randomization for security patrolling with dynamic execution uncertainty

In recent years there has been extensive research on game-theoretic models for infrastructure security. In time-critical domains where the security agency needs to execute complex patrols, execution uncertainty(interruptions) affect the patroller's ability to carry out their planned schedules later. Indeed, experiments in this paper show that in some real-world domains, small fractions of execution uncertainty can have a dramatic impact. The contributions of this paper are threefold. First, we present a general Bayesian Stackelberg game model for security patrolling in dynamic uncertain domains, in which the uncertainty in the execution of patrols is represented using Markov Decision Processes. Second, we study the problem of computing Stackelberg equilibrium for this game. We show that when the utility functions have a certain separable structure, the defender's strategy space can be compactly represented, and we can reduce the problem to a polynomial-sized optimization problem. Finally, we apply our approach to fare inspection in the Los Angeles Metro Rail system. Numerical experiments show that patrol schedules generated using our approach outperform schedules generated using a previous algorithm that does not consider execution uncertainty.