IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v52y2004i4p597-605.html
   My bibliography  Save this article

An Ambush Game with an Unknown Number of Infiltrators

Author

Listed:
  • Vic Baston

    (Faculty of Mathematical Studies, University of Southampton, Highfield, Southampton SO17 1BJ, United Kingdom)

  • Kensaku Kikuta

    (Kobe University of Commerce, Gakuen-Nishi 8-2-1, Nishi, Kobe 651-2197, Japan)

Abstract

We consider problems in which a defender is attempting to protect a channel from infiltration by laying static underwater devices across the channel. These devices can detect infiltrators that come within a given distance of them, and it is assumed that an infiltrator so detected can be apprehended before he can fulfill his mission. Previous work has concentrated on cases in which there is just one infiltrator and the infiltrator knows both the number of devices and their detection radii, but the emphasis in this paper is on situations in which the defender does not know the number of infiltrators and the infiltrators have only partial information about the devices. It is shown that the defender has a strategy that is optimal against any number of infiltrators when the detection radii satisfy certain conditions and, in particular, when the detection radii all lie in specific intervals. In the latter case, the infiltrators can also act optimally with only partial information concerning the detection devices. In addition, we obtain results giving the number of infiltrators that will ensure that at least one gets through undetected for various types of partial information available to the infiltrators.

Suggested Citation

  • Vic Baston & Kensaku Kikuta, 2004. "An Ambush Game with an Unknown Number of Infiltrators," Operations Research, INFORMS, vol. 52(4), pages 597-605, August.
    • Handle: RePEc:inm:oropre:v:52:y:2004:i:4:p:597-605
    DOI: 10.1287/opre.1040.0122
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.1040.0122
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.1040.0122?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. V. J. Baston & F. A. Bostock, 1987. "A continuous game of ambush," Naval Research Logistics (NRL), John Wiley & Sons, vol. 34(5), pages 645-654, October.
    2. Zoroa, Noemi & Zoroa, Procopio & Jose Fernandez-Saez, M., 1999. "A generalization of Ruckle's results for an ambush game," European Journal of Operational Research, Elsevier, vol. 119(2), pages 353-364, December.
    3. William H. Ruckle & John R. Reay, 1981. "Ambushing Random Walks III: More Continuous Models," Operations Research, INFORMS, vol. 29(1), pages 121-129, February.
    4. Noemí Zoroa & Procopio Zoroa & José Fernández‐Sáez, 2001. "New results on a Ruckle problem in discrete games of ambush," Naval Research Logistics (NRL), John Wiley & Sons, vol. 48(1), pages 98-106, February.
    5. William H. Ruckle, 1981. "Ambushing Random Walks II: Continuous Models," Operations Research, INFORMS, vol. 29(1), pages 108-120, February.
    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. Garrec, Tristan, 2019. "Continuous patrolling and hiding games," European Journal of Operational Research, Elsevier, vol. 277(1), pages 42-51.
    2. Wang, Jian & Cui, Lei, 2023. "Patrolling games with coordination between monitoring devices and patrols," Reliability Engineering and System Safety, Elsevier, vol. 233(C).
    3. 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.
    4. Zoroa, N. & Fernández-Sáez, M.J. & Zoroa, P., 2012. "Patrolling a perimeter," European Journal of Operational Research, Elsevier, vol. 222(3), pages 571-582.
    5. Alpern, Steve & Lidbetter, Thomas & Papadaki, Katerina, 2019. "Optimizing periodic patrols against short attacks on the line and other networks," European Journal of Operational Research, Elsevier, vol. 273(3), pages 1065-1073.
    6. Katerina Papadaki & Steve Alpern & Thomas Lidbetter & Alec Morton, 2016. "Patrolling a Border," Operations Research, INFORMS, vol. 64(6), pages 1256-1269, December.
    7. Alpern, Steve & Fokkink, Robbert & Simanjuntak, Martin, 2016. "Optimal search and ambush for a hider who can escape the search region," European Journal of Operational Research, Elsevier, vol. 251(3), pages 707-714.
    8. Vic Baston & Kensaku Kikuta, 2009. "Technical Note---An Ambush Game with a Fat Infiltrator," Operations Research, INFORMS, vol. 57(2), pages 514-519, April.

    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. I.D. Woodward, 2003. "Discretization of the continuous ambush game," Naval Research Logistics (NRL), John Wiley & Sons, vol. 50(5), pages 515-529, August.
    2. Garrec, Tristan, 2019. "Continuous patrolling and hiding games," European Journal of Operational Research, Elsevier, vol. 277(1), pages 42-51.
    3. Vic Baston & Kensaku Kikuta, 2009. "Technical Note---An Ambush Game with a Fat Infiltrator," Operations Research, INFORMS, vol. 57(2), pages 514-519, April.
    4. V. J. Baston & F. A. Bostock, 1989. "A one‐dimensional helicopter‐submarine game," Naval Research Logistics (NRL), John Wiley & Sons, vol. 36(4), pages 479-490, August.
    5. K. T. Lee, 1990. "On ruckle's game of ambush," Naval Research Logistics (NRL), John Wiley & Sons, vol. 37(3), pages 355-363, June.
    6. Alpern, Steve & Fokkink, Robbert & Simanjuntak, Martin, 2016. "Optimal search and ambush for a hider who can escape the search region," European Journal of Operational Research, Elsevier, vol. 251(3), pages 707-714.
    7. Hohzaki, Ryusuke & Iida, Koji, 2001. "Optimal ambushing search for a moving target," European Journal of Operational Research, Elsevier, vol. 133(1), pages 120-129, August.
    8. Noemí Zoroa & Procopio Zoroa & José Fernández‐Sáez, 2001. "New results on a Ruckle problem in discrete games of ambush," Naval Research Logistics (NRL), John Wiley & Sons, vol. 48(1), pages 98-106, February.
    9. V. J. Baston & F. A. Bostock, 1987. "A continuous game of ambush," Naval Research Logistics (NRL), John Wiley & Sons, vol. 34(5), pages 645-654, October.
    10. Zoroa, Noemi & Zoroa, Procopio & Jose Fernandez-Saez, M., 2003. "Raid games across a set with cyclic order," European Journal of Operational Research, Elsevier, vol. 145(3), pages 684-692, March.
    11. Zoroa, Noemi & Zoroa, Procopio & Jose Fernandez-Saez, M., 1999. "A generalization of Ruckle's results for an ambush game," European Journal of Operational Research, Elsevier, vol. 119(2), pages 353-364, December.
    12. Katerina Papadaki & Steve Alpern & Thomas Lidbetter & Alec Morton, 2016. "Patrolling a Border," Operations Research, INFORMS, vol. 64(6), pages 1256-1269, December.
    13. Endre Csóka & Thomas Lidbetter, 2016. "The solution to an open problem for a caching game," Naval Research Logistics (NRL), John Wiley & Sons, vol. 63(1), pages 23-31, February.
    14. Oléron Evans, Thomas P. & Bishop, Steven R., 2013. "Static search games played over graphs and general metric spaces," European Journal of Operational Research, Elsevier, vol. 231(3), pages 667-689.
    15. Zoroa, N. & Fernández-Sáez, M.J. & Zoroa, P., 2012. "Patrolling a perimeter," European Journal of Operational Research, Elsevier, vol. 222(3), pages 571-582.
    16. 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.
    17. Alpern, Steve & Lidbetter, Thomas & Papadaki, Katerina, 2019. "Optimizing periodic patrols against short attacks on the line and other networks," European Journal of Operational Research, Elsevier, vol. 273(3), pages 1065-1073.

    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:52:y:2004:i:4:p:597-605. 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.