Equilibrium Refinement in Security Games with Arbitrary Scheduling Constraints

Significant research effort in security games has focused in devising strategies that perform well even when the attacker deviates from optimal (rational) behavior. In most of these frameworks, a price needs to be paid to ensure robustness against this unpredictability. However, equilibrium refinement is an attractive alternative to boost solution robustness at no cost even though it has not received as much attention in security game literature. In this framework, resources are strategically allocated to secure an optimal outcome against a rational adversary while simultaneously protecting other targets to ensure good outcomes against boundedly rational or constrained attackers. Unfortunately, existing approaches for equilibrium refinement in security games cannot effectively address scheduling constraints that arise frequently in real-world applications. In this paper, we aim to fill this gap and make several key contributions. First, we show that existing approaches for equilibrium refinement can fail in the presence of scheduling constraints. Second, we investigate the properties of the best response of the attacker. Third, we leverage these properties to devise novel iterative algorithms to compute the optimally refined equilibrium, with polynomially many calls to an LP oracle for zero-sum games. Finally, we conduct extensive experimental evaluations that showcase (i) the superior performance of our approach in the face of a boundedly rational attacker and (ii) the attractive scalability properties of our algorithm that can solve realistic-sized instances.