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Combined Series And Parallel Systems Subject To Individual Versus Overarching Defense And Attack

Author

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  • KJELL HAUSKEN

    (Faculty of Social Sciences, University of Stavanger, 4036 Stavanger, Norway)

Abstract

A system of components can be in series, parallel, or combined series/parallel. The components and system are protected individually and overarchingly by a defender, and attacked individually and overarchingly by an attacker. Both layers of protection have to be breached for an attack to be successful. Each component, and the system as a whole, have vulnerabilities determined by individual and overarching protection and attack. The agents choose their effort variables simultaneously and independently to maximize their utilities. Each component and the system have unit costs of protection and attack, and a contest intensity. We show for both the parallel and series systems that the defender always prefers overarching and individual protection and attack, while the attacker always prefers individual protection and attack. Analytical expressions are developed for the agents' effort variables, each individual component's vulnerability, and the system vulnerability. The expenditure ratio, between individual protection and attack, and overarching protection and attack, is shown to increase in the number of components for the parallel system, and decrease in the number of components for the series system. Special cases are considered and interpreted. Comparisons are made with only individual protection and attack. The model is applicable to determine how the defender and attacker should strike the balance between choosing efforts to protect and attack components individually versus overarchingly.

Suggested Citation

  • Kjell Hausken, 2013. "Combined Series And Parallel Systems Subject To Individual Versus Overarching Defense And Attack," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 30(02), pages 1-33.
    • Handle: RePEc:wsi:apjorx:v:30:y:2013:i:02:n:s021759591250056x
    DOI: 10.1142/S021759591250056X
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    Citations

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    Cited by:

    1. 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.
    2. 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).
    3. Hausken, Kjell, 2024. "Fifty Years of Operations Research in Defense," European Journal of Operational Research, Elsevier, vol. 318(2), pages 355-368.
    4. Abdolmajid Yolmeh & Melike Baykal-Gürsoy & Vicki Bier, 2023. "A decomposable resource allocation model with generalized overarching protections," Annals of Operations Research, Springer, vol. 320(1), pages 493-507, January.
    5. Ye, Zhi-Sheng & Peng, Rui & Wang, Wenbin, 2017. "Defense and attack of performance-sharing common bus systemsAuthor-Name: Zhai, Qingqing," European Journal of Operational Research, Elsevier, vol. 256(3), pages 962-975.
    6. 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.
    7. Mo, Huadong & Xie, Min & Levitin, Gregory, 2015. "Optimal resource distribution between protection and redundancy considering the time and uncertainties of attacks," European Journal of Operational Research, Elsevier, vol. 243(1), pages 200-210.

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