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Computing Optimal Strategies for a Search Game in Discrete Locations

Author

Listed:
  • Jake Clarkson

    (Centre Inria d’Université Côte d’Azur, 06902 Sophia Antipolis, France)

  • Kyle Y. Lin

    (Operations Research Department, Naval Postgraduate School, Monterey, California 93943)

Abstract

Consider a two-person zero-sum search game between a hider and a searcher. The hider hides among n discrete locations, and the searcher successively visits individual locations until finding the hider. Known to both players, a search at location i takes t i time units and detects the hider—if hidden there—independently with probability α i , for i = 1 , … , n . The hider aims to maximize the expected time until detection, whereas the searcher aims to minimize it. We present an algorithm to compute an optimal strategy for each player. We demonstrate the algorithm’s efficiency in a numerical study, in which we also study the characteristics of the optimal hiding strategy.

Suggested Citation

  • Jake Clarkson & Kyle Y. Lin, 2025. "Computing Optimal Strategies for a Search Game in Discrete Locations," INFORMS Journal on Computing, INFORMS, vol. 37(3), pages 666-683, May.
    • Handle: RePEc:inm:orijoc:v:37:y:2025:i:3:p:666-683
    DOI: 10.1287/ijoc.2023.0155
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    References listed on IDEAS

    as
    1. Steve Alpern & Thomas Lidbetter, 2013. "Mining Coal or Finding Terrorists: The Expanding Search Paradigm," Operations Research, INFORMS, vol. 61(2), pages 265-279, April.
    2. Steve Alpern & Thomas Lidbetter, 2015. "Optimal Trade-Off Between Speed and Acuity When Searching for a Small Object," Operations Research, INFORMS, vol. 63(1), pages 122-133, February.
    3. Alpern, Steven & Lidbetter, Thomas, 2015. "Optimal trade-off between speed and acuity when searching for a small object," LSE Research Online Documents on Economics 61504, London School of Economics and Political Science, LSE Library.
    4. Jake Clarkson & Kyle Y. Lin & Kevin D. Glazebrook, 2023. "A Classical Search Game in Discrete Locations," Mathematics of Operations Research, INFORMS, vol. 48(2), pages 687-707, May.
    5. Steve Alpern, 2011. "Find-and-Fetch Search on a Tree," Operations Research, INFORMS, vol. 59(5), pages 1258-1268, October.
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    7. Vic Baston & Kensaku Kikuta, 2015. "Search games on a network with travelling and search costs," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(2), pages 347-365, May.
    8. D. M. Roberts & J. C. Gittins, 1978. "The search for an intelligent evader: Strategies for searcher and evader in the two‐region problem," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 25(1), pages 95-106, March.
    9. Lidbetter, Thomas, 2013. "Search games with multiple hidden objects," LSE Research Online Documents on Economics 55103, London School of Economics and Political Science, LSE Library.
    10. Lidbetter, Thomas & Lin, Kyle Y., 2019. "Searching for multiple objects in multiple locations," European Journal of Operational Research, Elsevier, vol. 278(2), pages 709-720.
    11. Jake Clarkson & Kevin D. Glazebrook & Kyle Y. Lin, 2020. "Fast or Slow: Search in Discrete Locations with Two Search Modes," Operations Research, INFORMS, vol. 68(2), pages 552-571, March.
    12. Lisa Hellerstein & Thomas Lidbetter & Daniel Pirutinsky, 2019. "Solving Zero-Sum Games Using Best-Response Oracles with Applications to Search Games," Operations Research, INFORMS, vol. 67(3), pages 731-743, May.
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