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Efficiency of Even Separation of Parallel Elements with Variable Contest Intensity

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  • Kjell Hausken
  • Gregory Levitin

Abstract

The article considers strategic defense and attack of a system that can be separated into parallel elements. The defender distributes its resource between separation and protecting the elements from outside attacks. The vulnerability of each element is determined by an attacker‐defender contest success function, which depends on a contest intensity that may increase or decrease through the separation process. The article determines criteria of separation efficiency for systems without performance redundancy and 1‐out‐of‐N and Q‐out‐of‐N systems with performance redundancy. For the systems with performance redundancy the cases of expected damage proportional to the probability that the demand is not met, and expected damage proportional to the unsupplied demand, are considered.

Suggested Citation

  • Kjell Hausken & Gregory Levitin, 2008. "Efficiency of Even Separation of Parallel Elements with Variable Contest Intensity," Risk Analysis, John Wiley & Sons, vol. 28(5), pages 1477-1486, October.
    • Handle: RePEc:wly:riskan:v:28:y:2008:i:5:p:1477-1486
    DOI: 10.1111/j.1539-6924.2008.01090.x
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    References listed on IDEAS

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    1. Hausken, Kjell, 2008. "Strategic defense and attack for series and parallel reliability systems," European Journal of Operational Research, Elsevier, vol. 186(2), pages 856-881, April.
    2. Vicki Bier & Santiago Oliveros & Larry Samuelson, 2007. "Choosing What to Protect: Strategic Defensive Allocation against an Unknown Attacker," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 9(4), pages 563-587, August.
    3. Azaiez, M.N. & Bier, Vicki M., 2007. "Optimal resource allocation for security in reliability systems," European Journal of Operational Research, Elsevier, vol. 181(2), pages 773-786, September.
    4. Kjell Hausken, 2005. "Production and Conflict Models Versus Rent-Seeking Models," Public Choice, Springer, vol. 123(1), pages 59-93, April.
    5. Hirshleifer, Jack, 1995. "Anarchy and Its Breakdown," Journal of Political Economy, University of Chicago Press, vol. 103(1), pages 26-52, February.
    6. Stergios Skaperdas, 1996. "Contest success functions (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 7(2), pages 283-290.
    7. Hausken, Kjell, 2008. "Strategic defense and attack for reliability systems," Reliability Engineering and System Safety, Elsevier, vol. 93(11), pages 1740-1750.
    8. Hausken, Kjell, 2006. "Income, interdependence, and substitution effects affecting incentives for security investment," Journal of Accounting and Public Policy, Elsevier, vol. 25(6), pages 629-665.
    9. Kunreuther, Howard & Heal, Geoffrey, 2003. "Interdependent Security," Journal of Risk and Uncertainty, Springer, vol. 26(2-3), pages 231-249, March-May.
    10. Levitin, Gregory, 2003. "Optimal allocation of multi-state elements in linear consecutively connected systems with vulnerable nodes," European Journal of Operational Research, Elsevier, vol. 150(2), pages 406-419, October.
    11. Kjell Hausken, 2004. "Mutual Raiding of Production and the Emergence of Exchange," Economic Inquiry, Western Economic Association International, vol. 42(4), pages 572-586, October.
    12. Kjell Hausken, 2002. "Probabilistic Risk Analysis and Game Theory," Risk Analysis, John Wiley & Sons, vol. 22(1), pages 17-27, February.
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    Citations

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    Cited by:

    1. Hausken, Kjell, 2010. "Strategic Defense and Attack for Series and Parallel Reliability Systems: Reply on Comment," MPRA Paper 25497, University Library of Munich, Germany, revised 02 Oct 2010.
    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.
    3. Kjell Hausken & Jonathan W. Welburn, 2021. "Attack and Defense Strategies in Cyber War Involving Production and Stockpiling of Zero-Day Cyber Exploits," Information Systems Frontiers, Springer, vol. 23(6), pages 1609-1620, December.
    4. Kjell Hausken & Fei He, 2016. "On the Effectiveness of Security Countermeasures for Critical Infrastructures," Risk Analysis, John Wiley & Sons, vol. 36(4), pages 711-726, April.
    5. Gregory Levitin & Kjell Hausken, 2010. "Resource Distribution in Multiple Attacks Against a Single Target," Risk Analysis, John Wiley & Sons, vol. 30(8), pages 1231-1239, August.
    6. Dan Kovenock & Brian Roberson, 2012. "Strategic Defense And Attack For Series And Parallel Reliability Systems: Comment," Defence and Peace Economics, Taylor & Francis Journals, vol. 23(5), pages 507-515, October.
    7. Guizhou Wang & Jonathan W. Welburn & Kjell Hausken, 2020. "A Two-Period Game Theoretic Model of Zero-Day Attacks with Stockpiling," Games, MDPI, vol. 11(4), pages 1-26, December.
    8. Hausken, Kjell & Levitin, Gregory, 2009. "Protection vs. false targets in series systems," Reliability Engineering and System Safety, Elsevier, vol. 94(5), pages 973-981.
    9. Gregory Levitin & Maxim Finkelstein, 2017. "A new stress–strength model for systems subject to stochastic shocks," Journal of Risk and Reliability, , vol. 231(2), pages 172-179, April.
    10. 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.
    11. Gregory Levitin & Liudong Xing & Hong‐Zhong Huang, 2019. "Security of Separated Data in Cloud Systems with Competing Attack Detection and Data Theft Processes," Risk Analysis, John Wiley & Sons, vol. 39(4), pages 846-858, April.
    12. Kjell Hausken, 2019. "A Game Theoretic Model of Adversaries and Media Manipulation," Games, MDPI, vol. 10(4), pages 1-15, December.
    13. Kjell Hausken, 2012. "Strategic defense and attack for series and parallel reliability systems: reply 1 to comment 1," Defence and Peace Economics, Taylor & Francis Journals, vol. 23(5), pages 525-531, October.

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