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A Differential Game Related to Terrorism: Nash and Stackelberg Strategies

Author

Listed:
  • A. J. Novak

    (University of Vienna)

  • G. Feichtinger

    (Vienna University of Technology)

  • G. Leitmann

    (University of California)

Abstract

The question of how best to prosecute the ‘war on terror’ leads to strategic interaction in an intertemporal setting. We consider a nonzero sum differential game between a government and a terrorist organisation. Due to the state-separability of the game we are able to determine Nash and Stackelberg solutions in analytic form. Their comparison as well as the sensitivity analysis deliver interesting insight into the design of efficient measures to combat terror.

Suggested Citation

  • A. J. Novak & G. Feichtinger & G. Leitmann, 2010. "A Differential Game Related to Terrorism: Nash and Stackelberg Strategies," Journal of Optimization Theory and Applications, Springer, vol. 144(3), pages 533-555, March.
    • Handle: RePEc:spr:joptap:v:144:y:2010:i:3:d:10.1007_s10957-009-9643-z
    DOI: 10.1007/s10957-009-9643-z
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    References listed on IDEAS

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    1. 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, October.
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    3. G. Feichtinger & A. J. Novak, 2008. "Terror and Counterterror Operations: Differential Game with Cyclical Nash Solution," Journal of Optimization Theory and Applications, Springer, vol. 139(3), pages 541-556, December.
    4. 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, October.
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    Cited by:

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    3. Bertrand Crettez & Naila Hayek, 2014. "Terrorists’ Eradication Versus Perpetual Terror War," Journal of Optimization Theory and Applications, Springer, vol. 160(2), pages 679-702, February.
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    6. João Ricardo Faria & Emilson C. D. Silva & Daniel G. Arce, 2017. "Intertemporal Versus Spatial Externalities in Counterterror Policy Games," Dynamic Games and Applications, Springer, vol. 7(3), pages 402-421, September.
    7. Szilárd Nagy, 2013. "Stackelberg equilibria via variational inequalities and projections," Journal of Global Optimization, Springer, vol. 57(3), pages 821-828, November.
    8. Nageswara S. V. Rao & Stephen W. Poole & Chris Y. T. Ma & Fei He & Jun Zhuang & David K. Y. Yau, 2016. "Defense of Cyber Infrastructures Against Cyber‐Physical Attacks Using Game‐Theoretic Models," Risk Analysis, John Wiley & Sons, vol. 36(4), pages 694-710, April.
    9. Naïla Hayek, 2011. "A Generalization of Mixed Problems with an Application to Multiobjective Optimal Control," Journal of Optimization Theory and Applications, Springer, vol. 150(3), pages 498-515, September.
    10. Eduardo Mojica-Nava & Fredy Ruiz, 2021. "Stackelberg Population Dynamics: A Predictive-Sensitivity Approach," Games, MDPI, vol. 12(4), pages 1-15, November.
    11. João Ricardo Faria & Andreas Novak & Aniruddha Bagchi & Timothy Mathews, 2020. "The Refugee Game: The Relationship between Individual Security Expenditures and Collective Security," Games, MDPI, vol. 11(2), pages 1-13, June.
    12. Halkos, George & Papageorgiou, George, 2014. "Exploring the optimality of cyclical emission rates," MPRA Paper 54915, University Library of Munich, Germany.
    13. Gabriel Ruiz-Garzón & Rafaela Osuna-Gómez & Antonio Rufián-Lizana & Beatriz Hernández-Jiménez, 2020. "Approximate Efficient Solutions of the Vector Optimization Problem on Hadamard Manifolds via Vector Variational Inequalities," Mathematics, MDPI, vol. 8(12), pages 1-19, December.
    14. Catherine C. Langlois & Jean-Pierre P. Langlois, 2011. "The Escalation of Terror: Hate and the Demise of Terrorist Organizations," Conflict Management and Peace Science, Peace Science Society (International), vol. 28(5), pages 497-521, November.
    15. Li, Bo & Zhang, Ranran & Jin, Ting & Shu, Yadong, 2021. "Parametric approximate optimal control of uncertain differential game with application to counter terror," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    16. Sadana, Utsav & Reddy, Puduru Viswanadha & Zaccour, Georges, 2021. "Nash equilibria in nonzero-sum differential games with impulse control," European Journal of Operational Research, Elsevier, vol. 295(2), pages 792-805.
    17. Herbert Dawid & Engelbert Dockner & Richard Hartl & Josef Haunschmied & Ulrike Leopold-Wildburger & Mikulas Luptacik & Alexander Mehlmann & Alexia Prskawetz & Marion Rauner & Gerhard Sorger & Gernot T, 2010. "Gustav Feichtinger celebrates his 70th birthday," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 18(4), pages 437-451, December.
    18. Abd El-Monem A. Megahed, 2019. "The Stackelberg differential game for counter-terrorism," Quality & Quantity: International Journal of Methodology, Springer, vol. 53(1), pages 207-220, January.

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