Dynamic Games and Applications

, Volume 7, Issue 4, pp 578–593 | Cite as

Differential Terror Queue Games

  • Stefan WrzaczekEmail author
  • Edward H. Kaplan
  • Jonathan P. Caulkins
  • Andrea Seidl
  • Gustav Feichtinger


We present models of differential terror queue games, wherein terrorists seek to determine optimal attack rates over time, while simultaneously the government develops optimal counterterror staffing levels. The number of successful and interdicted terror attacks is determined via an underlying dynamic terror queue model. Different information structures and commitment abilities derive from different assumptions regarding what the players in the game can and cannot deduce about the underlying model. We compare and explain the impact of different information structures, i.e., open loop, closed loop, and asymmetric. 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 different cases. Using recently assembled data describing both terror attack and staffing levels, we compare the differential game models to each other as well as to the optimal control model of Seidl et al. (Eur J Oper Res 248:246–256, 2016). The paper concludes with a discussion of the lessons learned from the entire modeling exercise.


Counterterrorism Differential games Queues Intelligence 



This research was supported by the Austrian Science Fund (FWF) under Grants P25979-N25 and P25275-G11.


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Stefan Wrzaczek
    • 1
    Email author
  • Edward H. Kaplan
    • 2
  • Jonathan P. Caulkins
    • 3
  • Andrea Seidl
    • 4
  • Gustav Feichtinger
    • 1
    • 5
  1. 1.Wittgenstein Centre for Demography and Global Human Capital (IIASA, VID/ÖAW, WU), Vienna Institute of DemographyAustrian Academy of SciencesViennaAustria
  2. 2.Yale School of Management, Yale School of Public HealthYale School of Engineering and Applied ScienceNew HavenUSA
  3. 3.H. John Heinz III College, Carnegie Mellon UniversityPittsburghUSA
  4. 4.Department of Business AdministrationUniversity of ViennaViennaAustria
  5. 5.Institute of Statistics and Mathematical Methods in EconomicsVienna University of TechnologyViennaAustria

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