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Terrorists’ Eradication Versus Perpetual Terror War

Author

Listed:
  • Bertrand Crettez

    (Panthéon-Assas University, Paris II)

  • Naila Hayek

    (Panthéon-Assas University, Paris II)

Abstract

We study an infinite-horizon sequential dynamic game where the players are a government and an international terrorist organization. We provide conditions for the existence of equilibria in which the terrorists’ resources are totally destroyed by a government’s strike. Specifically, we study strong eradication equilibria in which the government’s strike annihilates the terrorists’ resources, preventing the terrorists from acting. We also pay attention to weak eradication equilibria in which the terrorists’ resources are destroyed but in which the initial value of the terrorists’ strike is nevertheless positive. We also show the existence of an equilibrium in which war is perpetual between the government and the terrorists. Perpetual war can only coexist with weak eradication equilibria. For these cases, we provide conditions under which the government would be better off in a weak eradication equilibrium.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:160:y:2014:i:2:d:10.1007_s10957-013-0380-y
    DOI: 10.1007/s10957-013-0380-y
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    References listed on IDEAS

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    1. Hausken, Kjell, 2008. "Whether to attack a terrorist's resource stock today or tomorrow," Games and Economic Behavior, Elsevier, vol. 64(2), pages 548-564, November.
    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. Kjell Hausken & Jun Zhuang, 2011. "Defending Against a Stockpiling Terrorist," The Engineering Economist, Taylor & Francis Journals, vol. 56(4), pages 321-353.
    4. Blot, J. & Chebbi, H., 2000. "Discrete time Pontryagin Principles with Infinite Horizon," Papiers d'Economie Mathématique et Applications 2000.20, Université Panthéon-Sorbonne (Paris 1).
    5. Zhuang, Jun & Bier, Vicki M. & Alagoz, Oguzhan, 2010. "Modeling secrecy and deception in a multiple-period attacker-defender signaling game," European Journal of Operational Research, Elsevier, vol. 203(2), pages 409-418, June.
    6. K Hausken & J Zhuang, 2012. "The timing and deterrence of terrorist attacks due to exogenous dynamics," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 63(6), pages 726-735, June.
    7. 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.
    8. Moshe Kress & Roberto Szechtman, 2009. "Why Defeating Insurgencies Is Hard: The Effect of Intelligence in Counterinsurgency Operations---A Best-Case Scenario," Operations Research, INFORMS, vol. 57(3), pages 578-585, June.
    9. 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.
    10. 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.
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