IDEAS home Printed from https://ideas.repec.org/a/wsi/apjorx/v30y2013i02ns021759591250056x.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S021759591250056X
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S021759591250056X?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. 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.
    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. 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.
    6. 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.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wsi:apjorx:v:30:y:2013:i:02:n:s021759591250056x. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Tai Tone Lim (email available below). General contact details of provider: http://www.worldscinet.com/apjor/apjor.shtml .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.