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An Ambush Game with an Unknown Number of Infiltrators

Author

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  • 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
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    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.
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    Citations

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    Cited by:

    1. Vic Baston & Kensaku Kikuta, 2009. "Technical Note---An Ambush Game with a Fat Infiltrator," Operations Research, INFORMS, vol. 57(2), pages 514-519, April.
    2. 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.
    3. Zoroa, N. & Fernández-Sáez, M.J. & Zoroa, P., 2012. "Patrolling a perimeter," European Journal of Operational Research, Elsevier, vol. 222(3), pages 571-582.
    4. 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.
    5. 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.
    6. Garrec, Tristan, 2019. "Continuous patrolling and hiding games," European Journal of Operational Research, Elsevier, vol. 277(1), pages 42-51.
    7. Wang, Jian & Cui, Lei, 2023. "Patrolling games with coordination between monitoring devices and patrols," Reliability Engineering and System Safety, Elsevier, vol. 233(C).
    8. Katerina Papadaki & Steve Alpern & Thomas Lidbetter & Alec Morton, 2016. "Patrolling a Border," Operations Research, INFORMS, vol. 64(6), pages 1256-1269, December.

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