Security Games on a Plane

Abstract

Most existing models of Stackelberg security games ignore the underlying topology of the space in which targets and defence resources are located. As a result, allocation of resources is restricted to a discrete collection of exogenously defined targets. However, in many practical security settings, defense resources can be located on a continuous plane. Better defense solutions could therefore be potentially achieved by placing resources in a space outside of actual targets (e.g., between targets). To address this limitation, we propose a model called Security Game on a Plane (SGP) in which targets are distributed on a 2-dimensional plane, and security resources, to be allocated on the same plane, protect targets within a certain effective distance. We investigate the algorithmic aspects of SGP. We find that computing a strong Stackelberg equilibrium of an SGP is NP-hard even for zero-sum games, and these are inapproximable in general. On the positive side, we find an exact solution technique for general SGPs based on an existing approach, and develop a PTAS (polynomial-time approximation scheme) for zero-sum SGP to more fundamentally overcome the computational obstacle. Our experiments demonstrate the value of considering SGP and effectiveness of our algorithms.