IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v59y2011i5p1246-1257.html
   My bibliography  Save this article

Patrolling Games

Author

Listed:
  • Steve Alpern

    (Department of Mathematics and Management Science Group, Department of Management, London School of Economics and Political Science, London WC2A 2AE, United Kingdom)

  • Alec Morton

    (Management Science Group, Department of Management, London School of Economics and Political Science, London WC2A 2AE, United Kingdom)

  • Katerina Papadaki

    (Management Science Group, Department of Management, London School of Economics and Political Science, London WC2A 2AE, United Kingdom)

Abstract

A key operational problem for those charged with the security of vulnerable facilities (such as airports or art galleries) is the scheduling and deployment of patrols. Motivated by the problem of optimizing randomized, and thus unpredictable, patrols, we present a class of patrolling games. The facility to be patrolled can be thought of as a network or graph Q of interconnected nodes (e.g., rooms, terminals), and the Attacker can choose to attack any node of Q within a given time T . He requires m consecutive periods there, uninterrupted by the Patroller, to commit his nefarious act (and win). The Patroller can follow any path on the graph. Thus, the patrolling game is a win-lose game, where the Value is the probability that the Patroller successfully intercepts an attack, given best play on both sides. We determine analytically either the Value of the game, or bounds on the Value, for various classes of graphs, and we discuss possible extensions and generalizations.

Suggested Citation

  • Steve Alpern & Alec Morton & Katerina Papadaki, 2011. "Patrolling Games," Operations Research, INFORMS, vol. 59(5), pages 1246-1257, October.
    • Handle: RePEc:inm:oropre:v:59:y:2011:i:5:p:1246-1257
    DOI: 10.1287/opre.1110.0983
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.1110.0983
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.1110.0983?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
    ---><---

    References listed on IDEAS

    as
    1. R.J. Aumann & S. Hart (ed.), 2002. "Handbook of Game Theory with Economic Applications," Handbook of Game Theory with Economic Applications, Elsevier, edition 1, volume 3, number 3.
    2. Craig R. Fox & David Bardolet & Daniel Lieb, 2005. "Partition Dependence in Decision Analysis, Resource Allocation, and Consumer Choice," Springer Books, in: Rami Zwick & Amnon Rapoport (ed.), Experimental Business Research, chapter 0, pages 229-251, Springer.
    3. Gustav Feichtinger, 1983. "A Differential Games Solution to a Model of Competition Between a Thief and the Police," Management Science, INFORMS, vol. 29(6), pages 686-699, June.
    4. Gerald Brown & Matthew Carlyle & Javier Salmerón & Kevin Wood, 2006. "Defending Critical Infrastructure," Interfaces, INFORMS, vol. 36(6), pages 530-544, December.
    5. P. Goutal & A. Garnaev & G. Garnaeva, 1997. "On the Infiltration Game," International Journal of Game Theory, Springer;Game Theory Society, vol. 26(2), pages 215-221.
    6. John M. Auger, 1991. "An infiltration game on k arcs," Naval Research Logistics (NRL), John Wiley & Sons, vol. 38(4), pages 511-529, August.
    7. Kensaku Kikuta & William H. Ruckle, 2002. "Continuous accumulation games on discrete locations," Naval Research Logistics (NRL), John Wiley & Sons, vol. 49(1), pages 60-77, February.
    8. Kenneth Chelst, 1978. "An Algorithm for Deploying a Crime Directed (Tactical) Patrol Force," Management Science, INFORMS, vol. 24(12), pages 1314-1327, August.
    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. Laan, Corine M. & van der Mijden, Tom & Barros, Ana Isabel & Boucherie, Richard J. & Monsuur, Herman, 2017. "An interdiction game on a queueing network with multiple intruders," European Journal of Operational Research, Elsevier, vol. 260(3), pages 1069-1080.
    2. Lidbetter, Thomas, 2017. "On the approximation ratio of the Random Chinese Postman Tour for network search," European Journal of Operational Research, Elsevier, vol. 263(3), pages 782-788.

    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. Zoroa, N. & Fernández-Sáez, M.J. & Zoroa, P., 2012. "Patrolling a perimeter," European Journal of Operational Research, Elsevier, vol. 222(3), pages 571-582.
    2. Guzman, Cristobal & Riffo, Javiera & Telha, Claudio & Van Vyve, Mathieu, 2021. "A Sequential Stackelberg Game for Dynamic Inspection Problems," LIDAM Discussion Papers CORE 2021036, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. Manish Jain & Jason Tsai & James Pita & Christopher Kiekintveld & Shyamsunder Rathi & Milind Tambe & Fernando Ordóñez, 2010. "Software Assistants for Randomized Patrol Planning for the LAX Airport Police and the Federal Air Marshal Service," Interfaces, INFORMS, vol. 40(4), pages 267-290, August.
    4. Baykal-Gürsoy, Melike & Duan, Zhe & Poor, H. Vincent & Garnaev, Andrey, 2014. "Infrastructure security games," European Journal of Operational Research, Elsevier, vol. 239(2), pages 469-478.
    5. Alpern, Steven & Morton, Alec & Papadaki, Katerina, 2011. "Patrolling games," LSE Research Online Documents on Economics 32210, London School of Economics and Political Science, LSE Library.
    6. Zoroa, N. & Zoroa, P. & Fernández-Sáez, M.J., 2009. "Weighted search games," European Journal of Operational Research, Elsevier, vol. 195(2), pages 394-411, June.
    7. Kyle Y. Lin & Michael P. Atkinson & Timothy H. Chung & Kevin D. Glazebrook, 2013. "A Graph Patrol Problem with Random Attack Times," Operations Research, INFORMS, vol. 61(3), pages 694-710, June.
    8. Marco Faravelli & Randall Walsh, 2011. "Smooth Politicians And Paternalistic Voters: A Theory Of Large Elections," Levine's Working Paper Archive 786969000000000250, David K. Levine.
    9. Ding, Zhanwen & Shi, Guiping, 2009. "Cooperation in a dynamical adjustment of duopoly game with incomplete information," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 989-993.
    10. Jhinyoung Shin & Rajdeep Singh, 2010. "Corporate Disclosures: Strategic Donation of Information," International Review of Finance, International Review of Finance Ltd., vol. 10(3), pages 313-337, September.
    11. Mario Guajardo & Kurt Jörnsten & Mikael Rönnqvist, 2016. "Constructive and blocking power in collaborative transportation," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 38(1), pages 25-50, January.
    12. Sylvie Thoron, 2016. "Morality Beyond Social Preferences: Smithian Sympathy, Social Neuroscience and the Nature of Social Consciousness [La moralité au delà des préférences sociales. La sympathie Smithienne, les neurosc," Post-Print hal-01645043, HAL.
    13. Zhang, Chi & Ramirez-Marquez, José Emmanuel & Wang, Jianhui, 2015. "Critical infrastructure protection using secrecy – A discrete simultaneous game," European Journal of Operational Research, Elsevier, vol. 242(1), pages 212-221.
    14. Nan Xia & S. Rajagopalan, 2009. "Standard vs. Custom Products: Variety, Lead Time, and Price Competition," Marketing Science, INFORMS, vol. 28(5), pages 887-900, 09-10.
    15. Gerard Llobet & Javier Suarez, 2010. "Entrepreneurial Innovation, Patent Protection and Industry Dynamics," Working Papers wp2010_1001, CEMFI.
    16. Platz, Trine Tornøe & Østerdal, Lars Peter, 2017. "The curse of the first-in–first-out queue discipline," Games and Economic Behavior, Elsevier, vol. 104(C), pages 165-176.
    17. Jihui Chen & Qiang Fu, 2017. "Do exclusivity arrangements harm consumers?," Journal of Regulatory Economics, Springer, vol. 51(3), pages 311-339, June.
    18. Dinah Rosenberg & Eilon Solan & Nicolas Vieille, 2009. "Protocols with No Acknowledgment," Operations Research, INFORMS, vol. 57(4), pages 905-915, August.
    19. Yusuke Kamishiro & Roberto Serrano & Myrna Wooders, 2021. "Monopolists of scarce information and small group effectiveness in large quasilinear economies," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(4), pages 801-827, December.
    20. Xiaojun (Gene) Shan & Jun Zhuang, 2014. "Modeling Credible Retaliation Threats in Deterring the Smuggling of Nuclear Weapons Using Partial Inspection---A Three-Stage Game," Decision Analysis, INFORMS, vol. 11(1), pages 43-62, March.

    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:inm:oropre:v:59:y:2011:i:5:p:1246-1257. 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: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.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.