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Defence and attack of complex interdependent systems

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  • Kjell Hausken

Abstract

A defender defends and an attacker attacks each of n interdependent targets which can operate or fail and be in 2n possible states. Interdependence is modelled from each target to each other target. Despite such systems usually being analysed numerically, this paper succeeds in determining analytical solutions, accounting for unit effort costs, target values, and contest intensities. Increasing interdependence from some targets to some other targets induce both players to exert higher efforts into the former targets. For 100% interdependent targets, the attacker encounters a substitution effect. In contrast, for independent targets the defender encounters a substitution effect, defending the essential targets. For similarly advantaged players, increased target contest intensities cause higher efforts and lower expected utilities. Both players may withdraw in both 100% interdependent and independent systems. Applying the model to the US economy, we illustrate how interdependence between petroleum refineries, oil and gas extraction and air transportation impact defence, attack and expected utilities.

Suggested Citation

  • Kjell Hausken, 2019. "Defence and attack of complex interdependent systems," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 70(3), pages 364-376, March.
    • Handle: RePEc:taf:tjorxx:v:70:y:2019:i:3:p:364-376
    DOI: 10.1080/01605682.2018.1438763
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    Cited by:

    1. Valcamonico, Dario & Sansavini, Giovanni & Zio, Enrico, 2020. "Cooperative co-evolutionary approach to optimize recovery for improving resilience in multi-communities," Reliability Engineering and System Safety, Elsevier, vol. 197(C).
    2. Gabriel Kuper & Fabio Massacci & Woohyun Shim & Julian Williams, 2020. "Who Should Pay for Interdependent Risk? Policy Implications for Security Interdependence Among Airports," Risk Analysis, John Wiley & Sons, vol. 40(5), pages 1001-1019, May.
    3. Baraldi, Piero & Castellano, Andrea & Shokry, Ahmed & Gentile, Ugo & Serio, Luigi & Zio, Enrico, 2020. "A Feature Selection-based Approach for the Identification of Critical Components in Complex Technical Infrastructures: Application to the CERN Large Hadron Collider," Reliability Engineering and System Safety, Elsevier, vol. 201(C).
    4. Zhang, Xiaoxiong & Ye, Yanqing & Tan, Yuejin, 2020. "How to protect a genuine target against an attacker trying to detect false targets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 553(C).
    5. Bose, Gautam & Konrad, Kai A., 2020. "Devil take the hindmost: Deflecting attacks to other defenders," Reliability Engineering and System Safety, Elsevier, vol. 204(C).
    6. Ghorbani-Renani, Nafiseh & González, Andrés D. & Barker, Kash & Morshedlou, Nazanin, 2020. "Protection-interdiction-restoration: Tri-level optimization for enhancing interdependent network resilience," Reliability Engineering and System Safety, Elsevier, vol. 199(C).
    7. Nicola Dimitri, 2020. "Skills, Efficiency, and Timing in a Simple Attack and Defense Model," Decision Analysis, INFORMS, vol. 17(3), pages 227-234, September.
    8. Li, Qing & Li, Mingchu & Zhang, Runfa & Gan, Jianyuan, 2021. "A stochastic bilevel model for facility location-protection problem with the most likely interdiction strategy," Reliability Engineering and System Safety, Elsevier, vol. 216(C).
    9. Li, Qing & Li, Mingchu & Gong, Zhongqiang & Tian, Yuan & Zhang, Runfa, 2022. "Locating and protecting interdependent facilities to hedge against multiple non-cooperative limited choice attackers," Reliability Engineering and System Safety, Elsevier, vol. 223(C).
    10. Konrad, Kai A. & Morath, Florian, 2023. "How to preempt attacks in multi-front conflict with limited resources," European Journal of Operational Research, Elsevier, vol. 305(1), pages 493-500.
    11. Rui Peng & Di Wu & Mengyao Sun & Shaomin Wu, 2021. "An attack-defense game on interdependent networks," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 72(10), pages 2331-2341, October.
    12. Simon, Jay & Omar, Ayman, 2020. "Cybersecurity investments in the supply chain: Coordination and a strategic attacker," European Journal of Operational Research, Elsevier, vol. 282(1), pages 161-171.
    13. Gatmiry, Zohreh S. & Hafezalkotob, Ashkan & Khakzar bafruei, Morteza & Soltani, Roya, 2021. "Food web conservation vs. strategic threats: A security game approach," Ecological Modelling, Elsevier, vol. 442(C).
    14. Yan, Xihong & Ren, Xiaorong & Nie, Xiaofeng, 2022. "A budget allocation model for domestic airport network protection," Socio-Economic Planning Sciences, Elsevier, vol. 82(PB).
    15. Almoghathawi, Yasser & Selim, Shokri & Barker, Kash, 2023. "Community structure recovery optimization for partial disruption, functionality, and restoration in interdependent networks," Reliability Engineering and System Safety, Elsevier, vol. 229(C).
    16. Zhang, Xiaoxiong & Ding, Song & Ge, Bingfeng & Xia, Boyuan & Pedrycz, Witold, 2021. "Resource allocation among multiple targets for a defender-attacker game with false targets consideration," Reliability Engineering and System Safety, Elsevier, vol. 211(C).
    17. Wang, Shuliang & Gu, Xifeng & Luan, Shengyang & Zhao, Mingwei, 2021. "Resilience analysis of interdependent critical infrastructure systems considering deep learning and network theory," International Journal of Critical Infrastructure Protection, Elsevier, vol. 35(C).

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