IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v228y2013i1p262-272.html
   My bibliography  Save this article

Hybrid defensive resource allocations in the face of partially strategic attackers in a sequential defender–attacker game

Author

Listed:
  • Shan, Xiaojun
  • Zhuang, Jun

Abstract

Many models have been developed to study homeland security games between governments (defender) and terrorists (attacker, adversary, enemy), with the limiting assumption of the terrorists being rational or strategic. In this paper, we develop a novel hybrid model in which a centralized government allocates defensive resources among multiple potential targets to minimize total expected loss, in the face of a terrorist being either strategic or non-strategic. The attack probabilities of a strategic terrorist are endogenously determined in the model, while the attack probabilities of a non-strategic terrorist are exogenously provided. We study the robustness of defensive resource allocations by comparing the government’s total expected losses when: (a) the government knows the probability that the terrorist is strategic; (b) the government falsely believes that the terrorist is fully strategic, when the terrorist could be non-strategic; and (c) the government falsely believes that the terrorist is fully non-strategic, when the terrorist could be strategic. Besides providing six theorems to highlight the general results, we find that game models are generally preferred to non-game model even when the probability of a non-strategic terrorist is significantly greater than 50%. We conclude that defensive resource allocations based on game-theoretic models would not incur too much additional expected loss and thus more preferred, as compared to non-game-theoretic models.

Suggested Citation

  • Shan, Xiaojun & Zhuang, Jun, 2013. "Hybrid defensive resource allocations in the face of partially strategic attackers in a sequential defender–attacker game," European Journal of Operational Research, Elsevier, vol. 228(1), pages 262-272.
    • Handle: RePEc:eee:ejores:v:228:y:2013:i:1:p:262-272
    DOI: 10.1016/j.ejor.2013.01.029
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221713000763
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2013.01.029?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. Kreps, David M. & Milgrom, Paul & Roberts, John & Wilson, Robert, 1982. "Rational cooperation in the finitely repeated prisoners' dilemma," Journal of Economic Theory, Elsevier, vol. 27(2), pages 245-252, August.
    2. Hausken, Kjell, 2008. "Strategic defense and attack for series and parallel reliability systems," European Journal of Operational Research, Elsevier, vol. 186(2), pages 856-881, April.
    3. Chen Wang & Vicki M. Bier, 2011. "Target-Hardening Decisions Based on Uncertain Multiattribute Terrorist Utility," Decision Analysis, INFORMS, vol. 8(4), pages 286-302, December.
    4. Golany, Boaz & Kaplan, Edward H. & Marmur, Abraham & Rothblum, Uriel G., 2009. "Nature plays with dice - terrorists do not: Allocating resources to counter strategic versus probabilistic risks," European Journal of Operational Research, Elsevier, vol. 192(1), pages 198-208, January.
    5. Azaiez, M.N. & Bier, Vicki M., 2007. "Optimal resource allocation for security in reliability systems," European Journal of Operational Research, Elsevier, vol. 181(2), pages 773-786, September.
    6. Jun Zhuang & Vicki M. Bier, 2007. "Balancing Terrorism and Natural Disasters---Defensive Strategy with Endogenous Attacker Effort," Operations Research, INFORMS, vol. 55(5), pages 976-991, October.
    7. Berman, Oded & Gavious, Arieh, 2007. "Location of terror response facilities: A game between state and terrorist," European Journal of Operational Research, Elsevier, vol. 177(2), pages 1113-1133, March.
    8. Hausken, Kjell, 2008. "Strategic defense and attack for reliability systems," Reliability Engineering and System Safety, Elsevier, vol. 93(11), pages 1740-1750.
    9. Jian Hu & Tito Homem-de-Mello & Sanjay Mehrotra, 2011. "Risk-adjusted budget allocation models with application in homeland security," IISE Transactions, Taylor & Francis Journals, vol. 43(12), pages 819-839.
    10. 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.
    11. Powell, Robert, 2009. "Sequential, nonzero-sum "Blotto": Allocating defensive resources prior to attack," Games and Economic Behavior, Elsevier, vol. 67(2), pages 611-615, November.
    12. Brian Roberson, 2006. "The Colonel Blotto game," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 29(1), pages 1-24, September.
    13. 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.
    14. Edward H. Kaplan & Moshe Kress & Roberto Szechtman, 2010. "Confronting Entrenched Insurgents," Operations Research, INFORMS, vol. 58(2), pages 329-341, April.
    15. Wang, Xiaofang & Zhuang, Jun, 2011. "Balancing congestion and security in the presence of strategic applicants with private information," European Journal of Operational Research, Elsevier, vol. 212(1), pages 100-111, July.
    16. Gerald Brown & Matthew Carlyle & Douglas Diehl & Jeffrey Kline & Kevin Wood, 2005. "A Two-Sided Optimization for Theater Ballistic Missile Defense," Operations Research, INFORMS, vol. 53(5), pages 745-763, October.
    17. Hausken, Kjell & Zhuang, Jun, 2013. "The impact of disaster on the strategic interaction between company and government," European Journal of Operational Research, Elsevier, vol. 225(2), pages 363-376.
    18. Haphuriwat, N. & Bier, V.M., 2011. "Trade-offs between target hardening and overarching protection," European Journal of Operational Research, Elsevier, vol. 213(1), pages 320-328, August.
    19. Powell, Robert, 2007. "Defending against Terrorist Attacks with Limited Resources," American Political Science Review, Cambridge University Press, vol. 101(3), pages 527-541, August.
    20. Lawrence M. Wein, 2009. "OR Forum---Homeland Security: From Mathematical Models to Policy Implementation: The 2008 Philip McCord Morse Lecture," Operations Research, INFORMS, vol. 57(4), pages 801-811, August.
    21. Manas Baveja & Lawrence M. Wein, 2009. "An Effective Two-Finger, Two-Stage Biometric Strategy for the US-VISIT Program," Operations Research, INFORMS, vol. 57(5), pages 1068-1081, October.
    Full references (including those not matched with items on IDEAS)

    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. Hunt, Kyle & Zhuang, Jun, 2024. "A review of attacker-defender games: Current state and paths forward," European Journal of Operational Research, Elsevier, vol. 313(2), pages 401-417.
    2. Shan, Xiaojun & Zhuang, Jun, 2018. "Modeling cumulative defensive resource allocation against a strategic attacker in a multi-period multi-target sequential game," Reliability Engineering and System Safety, Elsevier, vol. 179(C), pages 12-26.
    3. Nikoofal, Mohammad E. & Zhuang, Jun, 2015. "On the value of exposure and secrecy of defense system: First-mover advantage vs. robustness," European Journal of Operational Research, Elsevier, vol. 246(1), pages 320-330.
    4. Hausken, Kjell, 2024. "Fifty Years of Operations Research in Defense," European Journal of Operational Research, Elsevier, vol. 318(2), pages 355-368.
    5. Mohammad E. Nikoofal & Mehmet Gümüs, 2015. "On the value of terrorist’s private information in a government’s defensive resource allocation problem," IISE Transactions, Taylor & Francis Journals, vol. 47(6), pages 533-555, June.
    6. 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.
    7. Peiqiu Guan & Jun Zhuang, 2015. "Modeling Public–Private Partnerships in Disaster Management via Centralized and Decentralized Models," Decision Analysis, INFORMS, vol. 12(4), pages 173-189, December.
    8. Talarico, Luca & Reniers, Genserik & Sörensen, Kenneth & Springael, Johan, 2015. "MISTRAL: A game-theoretical model to allocate security measures in a multi-modal chemical transportation network with adaptive adversaries," Reliability Engineering and System Safety, Elsevier, vol. 138(C), pages 105-114.
    9. Sushil Gupta & Martin K. Starr & Reza Zanjirani Farahani & Mahsa Mahboob Ghodsi, 2020. "Prevention of Terrorism–An Assessment of Prior POM Work and Future Potentials," Production and Operations Management, Production and Operations Management Society, vol. 29(7), pages 1789-1815, July.
    10. Kjell Hausken, 2014. "Individual versus overarching protection and attack of assets," 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. 22(1), pages 89-112, March.
    11. Mohammad E. Nikoofal & Jun Zhuang, 2012. "Robust Allocation of a Defensive Budget Considering an Attacker's Private Information," Risk Analysis, John Wiley & Sons, vol. 32(5), pages 930-943, May.
    12. Hausken, Kjell & Zhuang, Jun, 2013. "The impact of disaster on the strategic interaction between company and government," European Journal of Operational Research, Elsevier, vol. 225(2), pages 363-376.
    13. Bier, Vicki M. & Hausken, Kjell, 2013. "Defending and attacking a network of two arcs subject to traffic congestion," Reliability Engineering and System Safety, Elsevier, vol. 112(C), pages 214-224.
    14. Hausken, Kjell, 2017. "Special versus general protection and attack of parallel and series components," Reliability Engineering and System Safety, Elsevier, vol. 165(C), pages 239-256.
    15. Subhasish Chowdhury & Dan Kovenock & Roman Sheremeta, 2013. "An experimental investigation of Colonel Blotto games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 52(3), pages 833-861, April.
    16. Liang, Liang & Chen, Jingxian & Siqueira, Kevin, 2020. "Revenge or continued attack and defense in defender–attacker conflicts," European Journal of Operational Research, Elsevier, vol. 287(3), pages 1180-1190.
    17. Song, Cen & Zhuang, Jun, 2017. "N-stage security screening strategies in the face of strategic applicants," Reliability Engineering and System Safety, Elsevier, vol. 165(C), pages 292-301.
    18. Jie Xu & Jun Zhuang, 2016. "Modeling costly learning and counter-learning in a defender-attacker game with private defender information," Annals of Operations Research, Springer, vol. 236(1), pages 271-289, January.
    19. Wenzel, Lars & Wolf, André, 2013. "Protection against major catastrophes: An economic perspective," HWWI Research Papers 137, Hamburg Institute of International Economics (HWWI).
    20. Paulson, Elisabeth C. & Linkov, Igor & Keisler, Jeffrey M., 2016. "A game theoretic model for resource allocation among countermeasures with multiple attributes," European Journal of Operational Research, Elsevier, vol. 252(2), pages 610-622.

    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:eee:ejores:v:228:y:2013:i:1:p:262-272. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    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.