Differential Terror Queue Games

We present models of di erential terror queue games, wherein terrorists seek to determine optimal attack rates over time while simultaneously the government develops optimal counter terror sta ng levels. The number of successful and interdicted terror attacks are determined via an underlying uid terror queue model. Di erent information states and commitment abilities derive from di erent assumptions regarding what the players in the game can and cannot deduce about this underlying model. We consider three di erent possibilities: open-loop, where both the terrorists and the government have full information but must commit in advance to all future decisions when the game begins; a mixed structure whereby the terrorists are able to observe the total number of terror plots they have launched but are unaware of how many have already been detected by the government, while the government is only aware of terror plots they have discovered and unaware of undetected but in-progress terror plots; and the closed-loop structure whereby both players have full information over time. We characterize the optimal controls for both the terrorists and the government in terms of the associated state and costate variables, and deduce the costate equations that must be solved numerically to yield solutions to the game for the di erent information structures. Using recently assembled data describing both terror attack and sta ng levels, we compare the di erential game models to each other as well as to the optimal control model of Seidl et al [15]. The paper concludes with a discussion of the lessons learned from the entire modeling exercise.