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Modeling Arbitrary Layers of Continuous‐Level Defenses in Facing with Strategic Attackers

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  • Mohsen Golalikhani
  • Jun Zhuang

Abstract

We propose a novel class of game‐theoretic models for the optimal assignment of defensive resources in a game between a defender and an attacker. Compared to the other game‐theoretic models in the literature of defense allocation problems, the novelty of our model is that we allow the defender to assign her continuous‐level defensive resources to any subset (or arbitrary layers) of targets due to functional similarity or geographical proximity. We develop methods to solve for equilibrium, and illustrate our model using numerical examples. Compared to traditional models that only allow for individual target hardening, our results show that our model could significantly increase the defender's payoff, especially when the unit cost of defense is high.

Suggested Citation

  • Mohsen Golalikhani & Jun Zhuang, 2011. "Modeling Arbitrary Layers of Continuous‐Level Defenses in Facing with Strategic Attackers," Risk Analysis, John Wiley & Sons, vol. 31(4), pages 533-547, April.
    • Handle: RePEc:wly:riskan:v:31:y:2011:i:4:p:533-547
    DOI: 10.1111/j.1539-6924.2010.01531.x
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    Cited by:

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    4. Gary A. Ackerman & Jun Zhuang & Sitara Weerasuriya, 2017. "Cross‐Milieu Terrorist Collaboration: Using Game Theory to Assess the Risk of a Novel Threat," Risk Analysis, John Wiley & Sons, vol. 37(2), pages 342-371, February.
    5. Ridwan Al Aziz & Meilin He & Jun Zhuang, 2020. "An Attacker–defender Resource Allocation Game with Substitution and Complementary Effects," Risk Analysis, John Wiley & Sons, vol. 40(7), pages 1481-1506, July.
    6. 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.
    7. 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.
    8. Peiqiu Guan & Jun Zhuang, 2016. "Modeling Resources Allocation in Attacker‐Defender Games with “Warm Up” CSF," Risk Analysis, John Wiley & Sons, vol. 36(4), pages 776-791, April.
    9. Wu, Yipeng & Chen, Zhilong & Zhao, Xudong & Liu, Ying & Zhang, Ping & Liu, Yajiao, 2021. "Robust analysis of cascading failures in complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 583(C).
    10. Schlicher, Loe & Lurkin, Virginie, 2024. "Fighting pickpocketing using a choice-based resource allocation model," European Journal of Operational Research, Elsevier, vol. 315(2), pages 580-595.
    11. Wu, Yipeng & Chen, Zhilong & Dang, Junhu & Chen, Yicun & Zhao, Xudong & Zha, Lvying, 2022. "Allocation of defensive and restorative resources in electric power system against consecutive multi-target attacks," Reliability Engineering and System Safety, Elsevier, vol. 219(C).
    12. Zhang, Jing & Wang, Yan & Zhuang, Jun, 2021. "Modeling multi-target defender-attacker games with quantal response attack strategies," Reliability Engineering and System Safety, Elsevier, vol. 205(C).
    13. Qingqing Zhai & Rui Peng & Jun Zhuang, 2020. "Defender–Attacker Games with Asymmetric Player Utilities," Risk Analysis, John Wiley & Sons, vol. 40(2), pages 408-420, February.
    14. César Gil & David Rios Insua & Jesus Rios, 2016. "Adversarial Risk Analysis for Urban Security Resource Allocation," Risk Analysis, John Wiley & Sons, vol. 36(4), pages 727-741, April.
    15. Peiqiu Guan & Jing Zhang & Vineet M. Payyappalli & Jun Zhuang, 2018. "Modeling and Validating Public–Private Partnerships in Disaster Management," Decision Analysis, INFORMS, vol. 15(2), pages 55-71, June.
    16. Hunt, Kyle & Agarwal, Puneet & Zhuang, Jun, 2022. "On the adoption of new technology to enhance counterterrorism measures: An attacker–defender game with risk preferences," Reliability Engineering and System Safety, Elsevier, vol. 218(PB).
    17. Lin, Chen & Xiao, Hui & Peng, Rui & Xiang, Yisha, 2021. "Optimal defense-attack strategies between M defenders and N attackers: A method based on cumulative prospect theory," Reliability Engineering and System Safety, Elsevier, vol. 210(C).

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