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Individual versus overarching protection and attack of assets

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  • Kjell Hausken

Abstract

Two agents protect and attack a collection of assets overarchingly versus individually. Examples of overarching protection are border security, counter intelligence, and public health measures. Both layers of protection have to be breached for an attack to be successful. We consider a simultaneous game, and a two period game with overarching contest in period 1 and individual contests in period 2 if the attacker wins period 1. With reasonable assumptions, such as contest intensities not exceeding one, the defender prefers two protection layers, while the attacker prefers one protection layer. When the unit effort costs of overarching protection and attack are equal, and the agents’ valuations for each asset are equal, in the simultaneous game defender and attacker efforts are equal in the overarching contest. In contrast, for the two period game, the defender invests more than the attacker in the overarching contest to prevent the occurrence of period 2. If the attacker nevertheless wins period 1, both agents exert larger efforts in period 2 compared with the individual contests in the simultaneous game. Framed within the Colonel Blotto literature, the attacker must win the first battlefield (overarching contest) in order to engage in the contests over the n other battlefields (individual contests). Copyright Springer-Verlag Berlin Heidelberg 2014

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  • 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.
  • Handle: RePEc:spr:cejnor:v:22:y:2014:i:1:p:89-112
    DOI: 10.1007/s10100-012-0271-6
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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. Subhasish M Chowdhury & Dan Kovenock & David Rojo Arjona & Nathaniel T Wilcox, 2021. "Focality and Asymmetry in Multi-Battle Contests," The Economic Journal, Royal Economic Society, vol. 131(636), pages 1593-1619.
    3. 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).
    4. 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.
    5. 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.
    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. 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.
    8. 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.
    9. 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.
    10. 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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