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Technical Note---An Ambush Game with a Fat Infiltrator

Author

Listed:
  • Vic Baston

    (School of Mathematics, University of Southampton, Southampton SO17 1BJ, United Kingdom)

  • Kensaku Kikuta

    (School of Business Administration, University of Hyogo, Kobe 651-2197, Japan)

Abstract

This paper concerns a two-person zero-sum game between an infiltrator and a defender. The infiltrator wants to pass through a channel, while the defender wants to detect the infiltrator by laying static underwater devices across the channel. Previous work assumed the infiltrator has zero width. We consider an extension when the infiltrator has a positive width, and a proportion of its width needs to be detected by the underwater devices for a positive identification. We show that the positive-width problem reduces to the zero-width problem by an appropriate transformation.

Suggested Citation

  • Vic Baston & Kensaku Kikuta, 2009. "Technical Note---An Ambush Game with a Fat Infiltrator," Operations Research, INFORMS, vol. 57(2), pages 514-519, April.
    • Handle: RePEc:inm:oropre:v:57:y:2009:i:2:p:514-519
    DOI: 10.1287/opre.1080.0569
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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. William H. Ruckle & John R. Reay, 1981. "Ambushing Random Walks III: More Continuous Models," Operations Research, INFORMS, vol. 29(1), pages 121-129, February.
    3. William H. Ruckle, 1981. "Ambushing Random Walks II: Continuous Models," Operations Research, INFORMS, vol. 29(1), pages 108-120, February.
    4. Vic Baston & Kensaku Kikuta, 2004. "An Ambush Game with an Unknown Number of Infiltrators," Operations Research, INFORMS, vol. 52(4), pages 597-605, August.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Garrec, Tristan, 2019. "Continuous patrolling and hiding games," European Journal of Operational Research, Elsevier, vol. 277(1), pages 42-51.
    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. 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.
    4. Katerina Papadaki & Steve Alpern & Thomas Lidbetter & Alec Morton, 2016. "Patrolling a Border," Operations Research, INFORMS, vol. 64(6), pages 1256-1269, December.
    5. Steve Alpern & Robbert Fokkink & Christos Pelekis, 2012. "A Proof of the Kikuta–Ruckle Conjecture on Cyclic Caching of Resources," Journal of Optimization Theory and Applications, Springer, vol. 153(3), pages 650-661, June.

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