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Differential Terror Queue Games

Author

Listed:
  • Stefan Wrzaczek

    (Austrian Academy of Sciences)

  • Edward H. Kaplan

    (Yale School of Engineering and Applied Science)

  • Jonathan P. Caulkins

    (H. John Heinz III College, Carnegie Mellon University)

  • Andrea Seidl

    (University of Vienna)

  • Gustav Feichtinger

    (Austrian Academy of Sciences
    Vienna University of Technology)

Abstract

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.

Suggested Citation

  • Stefan Wrzaczek & Edward H. Kaplan & Jonathan P. Caulkins & Andrea Seidl & Gustav Feichtinger, 2017. "Differential Terror Queue Games," Dynamic Games and Applications, Springer, vol. 7(4), pages 578-593, December.
    • Handle: RePEc:spr:dyngam:v:7:y:2017:i:4:d:10.1007_s13235-016-0195-1
    DOI: 10.1007/s13235-016-0195-1
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    References listed on IDEAS

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    1. R. Cellini & L. Lambertini, 2005. "R&D Incentives and Market Structure: Dynamic Analysis," Journal of Optimization Theory and Applications, Springer, vol. 126(1), pages 85-96, July.
    2. Dieter Grass & Jonathan P. Caulkins & Gustav Feichtinger & Gernot Tragler & Doris A. Behrens, 2008. "Optimal Control of Nonlinear Processes," Springer Books, Springer, number 978-3-540-77647-5, June.
    3. Seidl, Andrea & Kaplan, Edward H. & Caulkins, Jonathan P. & Wrzaczek, Stefan & Feichtinger, Gustav, 2016. "Optimal control of a terror queue," European Journal of Operational Research, Elsevier, vol. 248(1), pages 246-256.
    4. Viscusi, W Kip & Aldy, Joseph E, 2003. "The Value of a Statistical Life: A Critical Review of Market Estimates throughout the World," Journal of Risk and Uncertainty, Springer, vol. 27(1), pages 5-76, August.
    5. Kaplan, Edward H., 2013. "Staffing models for covert counterterrorism agencies," Socio-Economic Planning Sciences, Elsevier, vol. 47(1), pages 2-8.
    6. Jonathan S. Feinstein & Edward H. Kaplan, 2010. "Analysis of a Strategic Terror Organization," Journal of Conflict Resolution, Peace Science Society (International), vol. 54(2), pages 281-302, April.
    7. Edward H. Kaplan, 2010. "Terror Queues," Operations Research, INFORMS, vol. 58(4-part-1), pages 773-784, August.
    8. Enders,Walter & Sandler,Todd, 2012. "The Political Economy of Terrorism," Cambridge Books, Cambridge University Press, number 9780521181006, January.
    9. Daniel Jacobson & Edward H. Kaplan, 2007. "Suicide Bombings and Targeted Killings in (Counter-) Terror Games," Journal of Conflict Resolution, Peace Science Society (International), vol. 51(5), pages 772-792, October.
    10. Edward H. Kaplan, 2015. "Socially efficient detection of terror plots," Oxford Economic Papers, Oxford University Press, vol. 67(1), pages 104-115.
    11. Edward H. Kaplan & Moshe Kress & Roberto Szechtman, 2010. "Confronting Entrenched Insurgents," Operations Research, INFORMS, vol. 58(2), pages 329-341, April.
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    13. Dockner,Engelbert J. & Jorgensen,Steffen & Long,Ngo Van & Sorger,Gerhard, 2000. "Differential Games in Economics and Management Science," Cambridge Books, Cambridge University Press, number 9780521637329, January.
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    Cited by:

    1. Ebrahimnejad, Sadoullah & khanbaba, Amirhossein & Samimi, Sina, 2021. "Development of an Input-Output Model Considering Simultaneous Effect of Risks in Infrastructure under Dynamic Conditions," Reliability Engineering and System Safety, Elsevier, vol. 213(C).
    2. Gustav Feichtinger & Richard F. Hartl & Peter M. Kort & Andrea Seidl & Stefan Wrzaczek, 2022. "Asymmetric Information in a Capital Accumulation Differential Game with Spillover and Learning Effects," Journal of Optimization Theory and Applications, Springer, vol. 194(3), pages 878-895, September.

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