Modeling a multi-target attacker-defender game with multiple attack types

How to allocate limited defense resources effectively and efficiently to prevent damages is a critical and difficult problem, especially when faced with adaptive attackers and various attack types (methods that the attacker uses). There has been a growing amount of literature on studying the strategic interactions between attackers (terrorists) and defenders (government). This research presents a novel class of multi-target attacker-defender games where the attackers have multiple attacking options including assassination, armed assault, bombing/explosion, facility/infrastructure attack, hijacking, hostage taking, and unarmed assault. Different attack types may lead to different attack success probabilities, consequences, and effectiveness of defensive resource allocation. Faced with multiple attack types and adaptive attackers, the defender distributes a limited amount of resources to multiple targets to minimize the total expected loss in a sequential game as the first mover. We provide numerical illustrations for the model results. The model is illustrated by: (a) using historical terrorism and defensive investment data to estimate the model parameters, and (b) comparing the historical resource allocation with the model outputs. From the sensitivity analyses, we find that the defense cost effectiveness against the “Hijacking,†and “Bombing/Explosion†attack types play a critical role in decreasing the expected loss. The proposed multi-attack model leads to less expected loss than that of both the single-attack model and the historical allocation from the Urban Area Security Initiative (UASI). This paper provides new insights on modeling defensive resource allocation models related to adaptive adversaries.