IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v144y2010i3d10.1007_s10957-009-9643-z.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-009-9643-z
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10957-009-9643-z?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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, September.
    2. Keohane, Nathaniel O & Zeckhauser, Richard J, 2003. "The Ecology of Terror Defense," Journal of Risk and Uncertainty, Springer, vol. 26(2-3), pages 201-229, March-May.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Xing Gao & Weijun Zhong & Shue Mei, 2013. "Information Security Investment When Hackers Disseminate Knowledge," Decision Analysis, INFORMS, vol. 10(4), pages 352-368, December.
    2. Michael Caputo & Chen Ling, 2015. "Intrinsic Comparative Dynamics of Locally Differentiable Feedback Stackelberg Equilibria," Dynamic Games and Applications, Springer, vol. 5(1), pages 1-25, March.
    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.
    4. Marta Biancardi & Andrea Di Liddo & Giovanni Villani, 2022. "How do Fines and Their Enforcement on Counterfeit Products Affect Social Welfare?," Computational Economics, Springer;Society for Computational Economics, vol. 60(4), pages 1547-1573, December.
    5. Bolin , Kristian & Lindgren, Björn, 2015. "PARENTAL INVESTMENTS IN CHILD HEALTH – the importance of paternalistic altruism, child egoism and short-sightedness," Working Papers in Economics 640, University of Gothenburg, Department of Economics.
    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. João Ricardo Faria & Daniel Arce, 2021. "The Path of Terror Attacks," Games, MDPI, vol. 12(2), pages 1-11, April.
    2. George Halkos & George Papageorgiou, 2014. "Exploring the optimality of cyclical emission rates," DEOS Working Papers 1404, Athens University of Economics and Business.
    3. Kjell Hausken & Jun Zhuang, 2011. "Governments' and Terrorists' Defense and Attack in a T -Period Game," Decision Analysis, INFORMS, vol. 8(1), pages 46-70, March.
    4. Ouardighi, Fouad El & Sim, Jeong Eun & Kim, Bowon, 2016. "Pollution accumulation and abatement policy in a supply chain," European Journal of Operational Research, Elsevier, vol. 248(3), pages 982-996.
    5. Dawid, Herbert & Keoula, Michel Y. & Kopel, Michael & Kort, Peter M., 2015. "Product innovation incentives by an incumbent firm: A dynamic analysis," Journal of Economic Behavior & Organization, Elsevier, vol. 117(C), pages 411-438.
    6. Halkos, George & Papageorgiou, George, 2015. "Dynamical methods in Environmental and Resource Economics," MPRA Paper 67845, University Library of Munich, Germany.
    7. Kogan, Konstantin & El Ouardighi, Fouad & Herbon, Avi, 2017. "Production with learning and forgetting in a competitive environment," International Journal of Production Economics, Elsevier, vol. 189(C), pages 52-62.
    8. Engwerda, J.C., 2013. "A Numerical Algorithm to find All Scalar Feedback Nash Equilibria," Other publications TiSEM aa391d31-11df-4693-9583-1, Tilburg University, School of Economics and Management.
    9. J. C. Engwerda & Salmah, 2013. "Necessary and Sufficient Conditions for Feedback Nash Equilibria for the Affine-Quadratic Differential Game," Journal of Optimization Theory and Applications, Springer, vol. 157(2), pages 552-563, May.
    10. Engwerda, J.C. & Salmah, Y., 2010. "Necessary and Sufficient Conditions for Feedback Nash Equilibria for the Affine Quadratic Differential," Discussion Paper 2010-78, Tilburg University, Center for Economic Research.
    11. El Ouardighi, Fouad & Sim, Jeongeun & Kim, Bowon, 2021. "Pollution accumulation and abatement policies in two supply chains under vertical and horizontal competition and strategy types," Omega, Elsevier, vol. 98(C).
    12. Fouad El Ouardighi & Konstantin Kogan & Giorgio Gnecco & Marcello Sanguineti, 2018. "Commitment-Based Equilibrium Environmental Strategies Under Time-Dependent Absorption Efficiency," Group Decision and Negotiation, Springer, vol. 27(2), pages 235-249, April.
    13. Xing Gao & Weijun Zhong & Shue Mei, 2013. "Information Security Investment When Hackers Disseminate Knowledge," Decision Analysis, INFORMS, vol. 10(4), pages 352-368, December.
    14. George E. Halkos & George J. Papageorgiou, 2021. "Some Results on the Control of Polluting Firms According to Dynamic Nash and Stackelberg Patterns," Economies, MDPI, vol. 9(2), pages 1-13, May.
    15. Fouad El Ouardighi & Gary Erickson & Dieter Grass & Steffen Jørgensen, 2016. "Contracts and Information Structure in a Supply Chain with Operations and Marketing Interaction," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 18(04), pages 1-36, December.
    16. Wirl, Franz & Feichtinger, Gustav & Kort, Peter M., 2013. "Individual firm and market dynamics of CSR activities," Journal of Economic Behavior & Organization, Elsevier, vol. 86(C), pages 169-182.
    17. Jacob Engwerda, 2017. "A Numerical Algorithm to Calculate the Unique Feedback Nash Equilibrium in a Large Scalar LQ Differential Game," Dynamic Games and Applications, Springer, vol. 7(4), pages 635-656, December.
    18. 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.
    19. Dmitry Gromov & Ekaterina Gromova, 2017. "On a Class of Hybrid Differential Games," Dynamic Games and Applications, Springer, vol. 7(2), pages 266-288, June.
    20. Halkos, George & Papageorgiou, George, 2013. "Dynamic modeling of pulse fishing: A game theoretic approach," MPRA Paper 47871, University Library of Munich, Germany.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:joptap:v:144:y:2010:i:3:d:10.1007_s10957-009-9643-z. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.