IDEAS home Printed from https://ideas.repec.org/p/pur/prukra/1253.html
   My bibliography  Save this paper

Strategic Defense and Attack for Series and Parallel Reliability Systems: Comment

Author

Listed:
  • Dan Kovenock
  • Brian Roberson

Abstract

Hausken (2008a) formulates a contest-theoretic model of the attack and defense of a network of targets. This note identi es a technical error that invalidates Hausken's characterization of Nash equilibrium for a substantial portion of the parameter space that he examines and provides necessary conditions for his solution to form a pure- strategy Nash equilibrium. Many of the existing results in the contest-theoretic liter- ature on the attack and defense of networks of targets rely upon Hausken's (2008a) characterization and require corresponding parameter restrictions. When these restric- tions are not met, the analysis of Clark and Konrad (2007) and Kovenock and Roberson (2010a) provides a foundation for constructing mixed-strategy Nash equilibria.

Suggested Citation

  • Dan Kovenock & Brian Roberson, 2010. "Strategic Defense and Attack for Series and Parallel Reliability Systems: Comment," Purdue University Economics Working Papers 1253, Purdue University, Department of Economics.
  • Handle: RePEc:pur:prukra:1253
    as

    Download full text from publisher

    File URL: https://business.purdue.edu/research/Working-papers-series/2010/1253.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Lazear, Edward P & Rosen, Sherwin, 1981. "Rank-Order Tournaments as Optimum Labor Contracts," Journal of Political Economy, University of Chicago Press, vol. 89(5), pages 841-864, October.
    2. Che, Yeon-Koo & Gale, Ian, 2000. "Difference-Form Contests and the Robustness of All-Pay Auctions," Games and Economic Behavior, Elsevier, vol. 30(1), pages 22-43, January.
    3. 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.
    4. Michael R. Baye & Dan Kovenock & Casper G. Vries, 1996. "The all-pay auction with complete information," Springer Books, in: Roger D. Congleton & Arye L. Hillman & Kai A. Konrad (ed.), 40 Years of Research on Rent Seeking 1, pages 209-223, Springer.
    5. K Hausken & G Levitin, 2010. "Defence of homogeneous parallel multi-state systems subject to two sequential attacks," Journal of Risk and Reliability, , vol. 224(3), pages 171-183, September.
    6. Baye, Michael R & Kovenock, Dan & de Vries, Casper G, 1994. "The Solution to the Tullock Rent-Seeking Game When R Is Greater Than 2: Mixed-Strategy Equilibria and Mean Dissipation Rates," Public Choice, Springer, vol. 81(3-4), pages 363-380, December.
    7. Dan Kovenock & Brian Roberson & Roman M. Sheremeta, 2019. "The attack and defense of weakest-link networks," Public Choice, Springer, vol. 179(3), pages 175-194, June.
    8. Levitin, Gregory & Hausken, Kjell, 2009. "False targets vs. redundancy in homogeneous parallel systems," Reliability Engineering and System Safety, Elsevier, vol. 94(2), pages 588-595.
    9. Gregory Levitin & Kjell Hausken, 2009. "Intelligence and Impact Contests in Systems with Fake Targets," Defense & Security Analysis, Taylor & Francis Journals, vol. 25(2), pages 157-173, June.
    10. Brian Roberson, 2006. "The Colonel Blotto game," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 29(1), pages 1-24, September.
    11. Levitin, Gregory & Hausken, Kjell, 2010. "Influence of attacker's target recognition ability on defense strategy in homogeneous parallel systems," Reliability Engineering and System Safety, Elsevier, vol. 95(5), pages 565-572.
    12. Levitin, Gregory & Hausken, Kjell, 2009. "False targets efficiency in defense strategy," European Journal of Operational Research, Elsevier, vol. 194(1), pages 155-162, April.
    13. G Levitin & K Hausken, 2010. "Defence and attack of systems with variable attacker system structure detection probability," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 61(1), pages 124-133, January.
    14. Levitin, Gregory & Hausken, Kjell, 2009. "Parallel systems under two sequential attacks," Reliability Engineering and System Safety, Elsevier, vol. 94(3), pages 763-772.
    15. Hausken, Kjell & Levitin, Gregory, 2009. "Minmax defense strategy for complex multi-state systems," Reliability Engineering and System Safety, Elsevier, vol. 94(2), pages 577-587.
    16. Levitin, Gregory & Hausken, Kjell, 2008. "Protection vs. redundancy in homogeneous parallel systems," Reliability Engineering and System Safety, Elsevier, vol. 93(10), pages 1444-1451.
    17. Levitin, Gregory & Hausken, Kjell, 2009. "Meeting a demand vs. enhancing protections in homogeneous parallel systems," Reliability Engineering and System Safety, Elsevier, vol. 94(11), pages 1711-1717.
    18. Hausken, Kjell & Levitin, Gregory, 2009. "Protection vs. false targets in series systems," Reliability Engineering and System Safety, Elsevier, vol. 94(5), pages 973-981.
    19. Levitin, Gregory & Hausken, Kjell, 2009. "Intelligence and impact contests in systems with redundancy, false targets, and partial protection," Reliability Engineering and System Safety, Elsevier, vol. 94(12), pages 1927-1941.
    20. Guoqiang Tian, 2009. "The Existence of Equilibria in Games with Arbitrary Strategy Spaces and Payoffs: A Full Characterization," Levine's Working Paper Archive 814577000000000160, David K. Levine.
    21. 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.
    22. Hausken, Kjell, 2008. "Strategic defense and attack for reliability systems," Reliability Engineering and System Safety, Elsevier, vol. 93(11), pages 1740-1750.
    23. Monteiro, Paulo Klinger & Page Jr, Frank H., 2007. "Uniform payoff security and Nash equilibrium in compact games," Journal of Economic Theory, Elsevier, vol. 134(1), pages 566-575, May.
    24. Baye, Michael R & Kovenock, Dan & de Vries, Casper G, 1999. "The Incidence of Overdissipation in Rent-Seeking Contests," Public Choice, Springer, vol. 99(3-4), pages 439-454, June.
    25. Hausken, Kjell, 2010. "Defense and attack of complex and dependent systems," Reliability Engineering and System Safety, Elsevier, vol. 95(1), pages 29-42.
    26. K Hausken & G Levitin, 2009. "Parallel systems with different types of defence resource expenditure under two sequential attacks," Journal of Risk and Reliability, , vol. 223(1), pages 71-85, March.
    27. 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.
    28. Alcalde, José & Dahm, Matthias, 2010. "Rent seeking and rent dissipation: A neutrality result," Journal of Public Economics, Elsevier, vol. 94(1-2), pages 1-7, February.
    29. Peng, R. & Levitin, G. & Xie, M. & Ng, S.H., 2010. "Defending simple series and parallel systems with imperfect false targets," Reliability Engineering and System Safety, Elsevier, vol. 95(6), pages 679-688.
    30. Levitin, Gregory & Hausken, Kjell, 2010. "Separation in homogeneous systems with independent identical elements," European Journal of Operational Research, Elsevier, vol. 203(3), pages 625-634, June.
    31. R Peng & G Levitin & M Xie & S H Ng, 2011. "Optimal defence of single object with imperfect false targets," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(1), pages 134-141, January.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. Subhasish M. Chowdhury & Iryna Topolyan, 2013. "The Attack-and-Defence Group Contests," University of East Anglia Applied and Financial Economics Working Paper Series 049, School of Economics, University of East Anglia, Norwich, UK..
    2. 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.
    3. Dan Kovenock & Brian Roberson & Roman M. Sheremeta, 2019. "The attack and defense of weakest-link networks," Public Choice, Springer, vol. 179(3), pages 175-194, June.
    4. Deck, Cary & Foster, Joshua & Song, Hongwei, 2015. "Defense against an opportunistic challenger: Theory and experiments," European Journal of Operational Research, Elsevier, vol. 242(2), pages 501-513.
    5. Kjell Hausken, 2012. "Strategic Defense and Attack for Series and Parallel Reliability Systems: Reply to Rejoinder," Defence and Peace Economics, Taylor & Francis Journals, vol. 23(5), pages 517-519, October.
    6. Dan Kovenock & Brian Roberson, 2012. "Strategic Defense And Attack For Series And Parallel Reliability Systems: Rejoinder," Defence and Peace Economics, Taylor & Francis Journals, vol. 23(5), pages 521-524, October.
    7. Gatmiry, Zohreh S. & Hafezalkotob, Ashkan & Khakzar bafruei, Morteza & Soltani, Roya, 2021. "Food web conservation vs. strategic threats: A security game approach," Ecological Modelling, Elsevier, vol. 442(C).
    8. Subhasish M. Chowdhury & Iryna Topolyan, 2016. "The Attack-And-Defense Group Contests: Best Shot Versus Weakest Link," Economic Inquiry, Western Economic Association International, vol. 54(1), pages 548-557, January.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Chen, Shun & Zhao, Xudong & Chen, Zhilong & Hou, Benwei & Wu, Yipeng, 2022. "A game-theoretic method to optimize allocation of defensive resource to protect urban water treatment plants against physical attacks," International Journal of Critical Infrastructure Protection, Elsevier, vol. 36(C).
    2. 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.
    3. Levitin, Gregory & Hausken, Kjell, 2013. "Is it wise to leave some false targets unprotected?," Reliability Engineering and System Safety, Elsevier, vol. 112(C), pages 176-186.
    4. Peng, R. & Zhai, Q.Q. & Levitin, G., 2016. "Defending a single object against an attacker trying to detect a subset of false targets," Reliability Engineering and System Safety, Elsevier, vol. 149(C), pages 137-147.
    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. Levitin, Gregory & Hausken, Kjell, 2009. "Intelligence and impact contests in systems with redundancy, false targets, and partial protection," Reliability Engineering and System Safety, Elsevier, vol. 94(12), pages 1927-1941.
    7. Yan, Xihong & Ren, Xiaorong & Nie, Xiaofeng, 2022. "A budget allocation model for domestic airport network protection," Socio-Economic Planning Sciences, Elsevier, vol. 82(PB).
    8. Levitin, Gregory & Hausken, Kjell, 2010. "Influence of attacker's target recognition ability on defense strategy in homogeneous parallel systems," Reliability Engineering and System Safety, Elsevier, vol. 95(5), pages 565-572.
    9. Peng, Rui & Xiao, Hui & Guo, Jianjun & Lin, Chen, 2020. "Defending a parallel system against a strategic attacker with redundancy, protection and disinformation," Reliability Engineering and System Safety, Elsevier, vol. 193(C).
    10. Gao, Kaiye & Yan, Xiangbin & Liu, Xiang-dong & Peng, Rui, 2019. "Object defence of a single object with preventive strike of random effect," Reliability Engineering and System Safety, Elsevier, vol. 186(C), pages 209-219.
    11. Abdolmajid Yolmeh & Melike Baykal-Gürsoy, 2019. "Two-Stage Invest–Defend Game: Balancing Strategic and Operational Decisions," Decision Analysis, INFORMS, vol. 16(1), pages 46-66, March.
    12. Ben Yaghlane, Asma & Azaiez, M. Naceur, 2017. "Systems under attack-survivability rather than reliability: Concept, results, and applications," European Journal of Operational Research, Elsevier, vol. 258(3), pages 1156-1164.
    13. Levitin, Gregory & Hausken, Kjell, 2011. "Is it wise to protect false targets?," Reliability Engineering and System Safety, Elsevier, vol. 96(12), pages 1647-1656.
    14. 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.
    15. Konrad, Kai A. & Morath, Florian, 2023. "How to preempt attacks in multi-front conflict with limited resources," European Journal of Operational Research, Elsevier, vol. 305(1), pages 493-500.
    16. Konrad, Kai A. & Kovenock, Dan, 2009. "Multi-battle contests," Games and Economic Behavior, Elsevier, vol. 66(1), pages 256-274, May.
    17. Kai Konrad, 2012. "Information alliances in contests with budget limits," Public Choice, Springer, vol. 151(3), pages 679-693, June.
    18. Christian Ewerhart, 2015. "Mixed equilibria in Tullock contests," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 60(1), pages 59-71, September.
    19. Emmanuel Dechenaux & Dan Kovenock & Roman Sheremeta, 2015. "A survey of experimental research on contests, all-pay auctions and tournaments," Experimental Economics, Springer;Economic Science Association, vol. 18(4), pages 609-669, December.
    20. Zhang, Jing & Zhuang, Jun & Jose, Victor Richmond R., 2018. "The role of risk preferences in a multi-target defender-attacker resource allocation game," Reliability Engineering and System Safety, Elsevier, vol. 169(C), pages 95-104.

    More about this item

    Keywords

    Game theory; Reliability theory; OR in military; Con ict; Contest; Network; Colonel Blotto game;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D74 - Microeconomics - - Analysis of Collective Decision-Making - - - Conflict; Conflict Resolution; Alliances; Revolutions
    • H56 - Public Economics - - National Government Expenditures and Related Policies - - - National Security and War

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    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:pur:prukra:1253. 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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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: Business PHD (email available below). General contact details of provider: https://edirc.repec.org/data/kspurus.html .

    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.