IDEAS home Printed from https://ideas.repec.org/a/wly/navres/v36y1989i4p479-490.html
   My bibliography  Save this article

A one‐dimensional helicopter‐submarine game

Author

Listed:
  • V. J. Baston
  • F. A. Bostock

Abstract

The article considers a two‐person zero‐sum game in which a searcher with b bombs wishes to destroy a mobile hider. The players are restricted to move on a straight line with maximum speeds v and u satisfying v > u > 0; neither player can see the other but each knows the other's initial position. The bombs all have destructive radius R and there is a time lag T between the release of a bomb and the bomb exploding. The searcher gets 1 unit if the hider is destroyed and 0 if he survives. A solution is given for b = 1, and extended to b > 1 when the time lag is small. Various applications of the game are discussed.

Suggested Citation

  • 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.
    • Handle: RePEc:wly:navres:v:36:y:1989:i:4:p:479-490
    DOI: 10.1002/1520-6750(198908)36:43.0.CO;2-7
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/1520-6750(198908)36:43.0.CO;2-7
    Download Restriction: no
    File URL: https://libkey.io/10.1002/1520-6750(198908)36:43.0.CO;2-7?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. William H. Ruckle & John R. Reay, 1981. "Ambushing Random Walks III: More Continuous Models," Operations Research, INFORMS, vol. 29(1), pages 121-129, February.
    2. William H. Ruckle, 1981. "Ambushing Random Walks II: Continuous Models," Operations Research, INFORMS, vol. 29(1), pages 108-120, February.
    3. James N. Eagle, 1984. "The Optimal Search for a Moving Target When the Search Path Is Constrained," Operations Research, INFORMS, vol. 32(5), pages 1107-1115, October.
    Full references (including those not matched with items on IDEAS)

    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. Garrec, Tristan, 2019. "Continuous patrolling and hiding games," European Journal of Operational Research, Elsevier, vol. 277(1), pages 42-51.
    2. Vic Baston & Kensaku Kikuta, 2004. "An Ambush Game with an Unknown Number of Infiltrators," Operations Research, INFORMS, vol. 52(4), pages 597-605, August.
    3. I.D. Woodward, 2003. "Discretization of the continuous ambush game," Naval Research Logistics (NRL), John Wiley & Sons, vol. 50(5), pages 515-529, August.
    4. K. T. Lee, 1990. "On ruckle's game of ambush," Naval Research Logistics (NRL), John Wiley & Sons, vol. 37(3), pages 355-363, June.
    5. 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.
    6. 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.
    7. Vic Baston & Kensaku Kikuta, 2009. "Technical Note---An Ambush Game with a Fat Infiltrator," Operations Research, INFORMS, vol. 57(2), pages 514-519, April.
    8. Jing Li & Ming Dong & Yijiong Ren & Kaiqi Yin, 2015. "How patient compliance impacts the recommendations for colorectal cancer screening," Journal of Combinatorial Optimization, Springer, vol. 30(4), pages 920-937, November.
    9. Corine M. Laan & Ana Isabel Barros & Richard J. Boucherie & Herman Monsuur & Judith Timmer, 2019. "Solving partially observable agent‐intruder games with an application to border security problems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 66(2), pages 174-190, March.
    10. Michael P. Atkinson & Moshe Kress & Roberto Szechtman, 2017. "To catch an intruder: Part A—uncluttered scenario," Naval Research Logistics (NRL), John Wiley & Sons, vol. 64(1), pages 29-40, February.
    11. Malek Ebadi & Raha Akhavan-Tabatabaei, 2021. "Personalized Cotesting Policies for Cervical Cancer Screening: A POMDP Approach," Mathematics, MDPI, vol. 9(6), pages 1-20, March.
    12. Zong-Zhi Lin & James C. Bean & Chelsea C. White, 2004. "A Hybrid Genetic/Optimization Algorithm for Finite-Horizon, Partially Observed Markov Decision Processes," INFORMS Journal on Computing, INFORMS, vol. 16(1), pages 27-38, February.
    13. Yanling Chang & Alan Erera & Chelsea White, 2015. "A leader–follower partially observed, multiobjective Markov game," Annals of Operations Research, Springer, vol. 235(1), pages 103-128, December.
    14. Bourque, François-Alex, 2019. "Solving the moving target search problem using indistinguishable searchers," European Journal of Operational Research, Elsevier, vol. 275(1), pages 45-52.
    15. Stanley J. Benkoski & Michael G. Monticino & James R. Weisinger, 1991. "A survey of the search theory literature," Naval Research Logistics (NRL), John Wiley & Sons, vol. 38(4), pages 469-494, August.
    16. Lyn C. Thomas & James N. Eagle, 1995. "Criteria and approximate methods for path‐constrained moving‐target search problems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 42(1), pages 27-38, February.
    17. J F J Vermeulen & M van den Brink, 2005. "The search for an alerted moving target," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(5), pages 514-525, May.
    18. Turgay Ayer & Oguzhan Alagoz & Natasha K. Stout & Elizabeth S. Burnside, 2016. "Heterogeneity in Women’s Adherence and Its Role in Optimal Breast Cancer Screening Policies," Management Science, INFORMS, vol. 62(5), pages 1339-1362, May.
    19. James N. Eagle & Alan R. Washburn, 1991. "Cumulative search‐evasion games," Naval Research Logistics (NRL), John Wiley & Sons, vol. 38(4), pages 495-510, August.
    20. Zehra Önen Dumlu & Serpil Sayın & İbrahim Hakan Gürvit, 2023. "Screening for preclinical Alzheimer’s disease: Deriving optimal policies using a partially observable Markov model," Health Care Management Science, Springer, vol. 26(1), pages 1-20, March.

    More about this item

    Statistics

    Access and download statistics

    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:wly:navres:v:36:y:1989:i:4:p:479-490. 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: Wiley Content Delivery (email available below). General contact details of provider: https://doi.org/10.1002/(ISSN)1520-6750 .

    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.