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Optimal defense with variable number of overarching and individual protections

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  • Levitin, Gregory
  • Hausken, Kjell
  • Dai, Yuanshun

Abstract

The article considers a system consisting of identical elements. Each element can be protected individually. The groups of elements can have overarching protection. To destroy an element having both types of protections the attacker must always penetrate/destroy the overarching protection and then destroy the individual protection of the element. Both the attacker and the defender have limited resources. The resources needed to defend and attack the overarching protection are fixed, as is also the number of elements that can be protected by single overarching protection. The defender chooses the number of overarching protections and the number of individual protections within each protected group to minimize the expected damage caused by the attack. The attacker chooses the number of attacked overarching protections and after attacking the overarching protections it chooses the number of attacked elements to maximize the expected damage. The three period minmax game is formulated and an enumerative procedure for its solving is suggested. The influence of the game parameters on the optimal defense and attack strategies is discussed.

Suggested Citation

  • Levitin, Gregory & Hausken, Kjell & Dai, Yuanshun, 2014. "Optimal defense with variable number of overarching and individual protections," Reliability Engineering and System Safety, Elsevier, vol. 123(C), pages 81-90.
    • Handle: RePEc:eee:reensy:v:123:y:2014:i:c:p:81-90
    DOI: 10.1016/j.ress.2013.11.001
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    References listed on IDEAS

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    2. Kjell Hausken, 2019. "Special versus general protection and attack of two assets," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 29(4), pages 53-93.
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    4. 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).
    5. 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.
    6. Ouyang, Min & Xu, Min & Zhang, Chi & Huang, Shitong, 2017. "Mitigating electric power system vulnerability to worst-case spatially localized attacks," Reliability Engineering and System Safety, Elsevier, vol. 165(C), pages 144-154.
    7. Bose, Gautam & Konrad, Kai A., 2020. "Devil take the hindmost: Deflecting attacks to other defenders," Reliability Engineering and System Safety, Elsevier, vol. 204(C).
    8. Ramirez-Marquez, José Emmanuel & Li, Qing, 2018. "Locating and protecting facilities from intentional attacks using secrecyAuthor-Name: Zhang, Chi," Reliability Engineering and System Safety, Elsevier, vol. 169(C), pages 51-62.
    9. Lin, Chen & Xiao, Hui & Kou, Gang & Peng, Rui, 2020. "Defending a series system with individual protection, overarching protection, and disinformation," Reliability Engineering and System Safety, Elsevier, vol. 204(C).
    10. Dui, Hongyan & Si, Shubin & Wu, Shaomin & Yam, Richard C.M., 2017. "An importance measure for multistate systems with external factors," Reliability Engineering and System Safety, Elsevier, vol. 167(C), pages 49-57.
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    15. Ríos Insua, David & Cano, Javier & Pellot, Michael & Ortega, Ricardo, 2016. "Multithreat multisite protection: A security case study," European Journal of Operational Research, Elsevier, vol. 252(3), pages 888-899.
    16. Cao, Minhao & Guo, Jianjun & Xiao, Hui & Wu, Liang, 2022. "Reliability analysis and optimal generator allocation and protection strategy of a non-repairable power grid system," Reliability Engineering and System Safety, Elsevier, vol. 222(C).
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    18. 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.

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