IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v236y2016i1p271-28910.1007-s10479-014-1722-3.html
   My bibliography  Save this article

Modeling costly learning and counter-learning in a defender-attacker game with private defender information

Author

Listed:
  • Jie Xu
  • Jun Zhuang

    ()

Abstract

In asymmetric war scenarios (e.g., counter-terrorism), the adversary usually invests a significant time to learn the system structure and identify vulnerable components, before launching attacks. Traditional game-theoretic defender-attacker models either ignore such learning periods or the entailed costs. This paper fills the gap by analyzing the strategic interactions of the terrorist’s costly learning and defender’s counter-learning and defense strategies in a game with private defender information. Our model allows six possible attacker strategies: (a) attack immediately; (b) learn and attack; (c) learn and not attack; (d) learn and attack when appearing vulnerable and not attack when appearing invulnerable; (e) learn and not attack when appearing vulnerable and attack when appearing invulnerable; and (f) not attack. Our results show that four of the six strategies (a, d, e, f) are possible at equilibrium and the other two (b, c) are strictly dominated. Interestingly, we find that the counterintuitive strategy (e) could be at equilibrium, especially when the probability that the target appears vulnerable given it is invulnerable is sufficiently high. Our results also show that the attacker’s learning cost has a significant impact on both the attacker’s best responses and the defender’s equilibrium deception and defense strategies. Finally, we study the attacker’s values of perfect information and imperfect information, which provide additional insights for defense and counter-learning strategies. Copyright Springer Science+Business Media New York 2016

Suggested Citation

  • Jie Xu & Jun Zhuang, 2016. "Modeling costly learning and counter-learning in a defender-attacker game with private defender information," Annals of Operations Research, Springer, vol. 236(1), pages 271-289, January.
  • Handle: RePEc:spr:annopr:v:236:y:2016:i:1:p:271-289:10.1007/s10479-014-1722-3
    DOI: 10.1007/s10479-014-1722-3
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10479-014-1722-3
    Download Restriction: Access to full text is restricted to subscribers.

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

    References listed on IDEAS

    as
    1. repec:wly:riskan:v:33:y:2013:i:6:p:1083-1099 is not listed on IDEAS
    2. repec:cup:apsrev:v:101:y:2007:i:04:p:799-809_07 is not listed on IDEAS
    3. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
    4. Barry R. Cobb & Atin Basuchoudhary, 2009. "A Decision Analysis Approach to Solving the Signaling Game," Decision Analysis, INFORMS, vol. 6(4), pages 239-255, December.
    5. repec:eee:reensy:v:94:y:2009:i:5:p:973-981 is not listed on IDEAS
    6. Jun Zhuang & Vicki M. Bier, 2007. "Balancing Terrorism and Natural Disasters---Defensive Strategy with Endogenous Attacker Effort," Operations Research, INFORMS, vol. 55(5), pages 976-991, October.
    7. Zhuang, Jun & Bier, Vicki M. & Alagoz, Oguzhan, 2010. "Modeling secrecy and deception in a multiple-period attacker-defender signaling game," European Journal of Operational Research, Elsevier, vol. 203(2), pages 409-418, June.
    8. Powell, Robert, 2009. "Sequential, nonzero-sum "Blotto": Allocating defensive resources prior to attack," Games and Economic Behavior, Elsevier, vol. 67(2), pages 611-615, November.
    9. 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.
    10. Jun Zhuang & Vicki Bier, 2011. "Secrecy And Deception At Equilibrium, With Applications To Anti-Terrorism Resource Allocation," Defence and Peace Economics, Taylor & Francis Journals, vol. 22(1), pages 43-61.
    11. Vicki Bier & Naraphorn Haphuriwat, 2011. "Analytical method to identify the number of containers to inspect at U.S. ports to deter terrorist attacks," Annals of Operations Research, Springer, vol. 187(1), pages 137-158, July.
    12. repec:wly:riskan:v:30:y:2010:i:12:p:1737-1743 is not listed on IDEAS
    13. Prajit K. Dutta, 1999. "Strategies and Games: Theory and Practice," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262041693, October.
    14. Chen Wang & Vicki M. Bier, 2013. "Expert Elicitation of Adversary Preferences Using Ordinal Judgments," Operations Research, INFORMS, vol. 61(2), pages 372-385, April.
    15. Gerald Brown & Matthew Carlyle & Douglas Diehl & Jeffrey Kline & Kevin Wood, 2005. "A Two-Sided Optimization for Theater Ballistic Missile Defense," Operations Research, INFORMS, vol. 53(5), pages 745-763, October.
    16. Insua, Insua Rios & Rios, Jesus & Banks, David, 2009. "Adversarial Risk Analysis," Journal of the American Statistical Association, American Statistical Association, vol. 104(486), pages 841-854.
    17. Todd Sandler & Kevin Siqueira, 2006. "Global terrorism: deterrence versus pre-emption," Canadian Journal of Economics, Canadian Economics Association, vol. 39(4), pages 1370-1387, November.
    18. Shan, Xiaojun & Zhuang, Jun, 2013. "Hybrid defensive resource allocations in the face of partially strategic attackers in a sequential defender–attacker game," European Journal of Operational Research, Elsevier, vol. 228(1), pages 262-272.
    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. repec:eee:reensy:v:179:y:2018:i:c:p:62-73 is not listed on IDEAS
    2. repec:eee:ejores:v:262:y:2017:i:1:p:89-107 is not listed on IDEAS

    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:spr:annopr:v:236:y:2016:i:1:p:271-289:10.1007/s10479-014-1722-3. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Sonal Shukla) or (Rebekah McClure). General contact details of provider: http://www.springer.com .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.