IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v283y2020i2p783-794.html
   My bibliography  Save this article

Search for an immobile hider on a stochastic network

Author

Listed:
  • Garrec, Tristan
  • Scarsini, Marco

Abstract

Harry hides on an edge of a graph and does not move from there. Sally, starting from a known origin, tries to find him as soon as she can. Harry’s goal is to be found as late as possible. At any given time, each edge of the graph is either active or inactive, independently of the other edges, with a known probability of being active. This situation can be modeled as a zero-sum two-person stochastic game. We show that the game has a value and we provide upper and lower bounds for this value. Finally, by generalizing optimal strategies of the deterministic case, we provide more refined results for trees and Eulerian graphs.

Suggested Citation

  • Garrec, Tristan & Scarsini, Marco, 2020. "Search for an immobile hider on a stochastic network," European Journal of Operational Research, Elsevier, vol. 283(2), pages 783-794.
    • Handle: RePEc:eee:ejores:v:283:y:2020:i:2:p:783-794
    DOI: 10.1016/j.ejor.2019.11.040
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221719309518
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2019.11.040?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Steve Alpern & Thomas Lidbetter, 2019. "Approximate solutions for expanding search games on general networks," Annals of Operations Research, Springer, vol. 275(2), pages 259-279, April.
    2. Cao, Buyang, 1995. "Search-hide games on trees," European Journal of Operational Research, Elsevier, vol. 80(1), pages 175-183, January.
    3. Steve Alpern, 2011. "Find-and-Fetch Search on a Tree," Operations Research, INFORMS, vol. 59(5), pages 1258-1268, October.
    4. Kensaku Kikuta, 2004. "A search game on a cyclic graph," Naval Research Logistics (NRL), John Wiley & Sons, vol. 51(7), pages 977-993, October.
    5. J.C. Gittins & D.M. Roberts, 1979. "The search for an intelligent evader concealed in one of an arbitrary number of regions," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 26(4), pages 651-666, December.
    6. 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.
    7. Ljiljana Pavlović, 1995. "A search game on the union of graphs with immobile hider," Naval Research Logistics (NRL), John Wiley & Sons, vol. 42(8), pages 1177-1189, December.
    8. Steve Alpern & Thomas Lidbetter, 2014. "Searching a Variable Speed Network," Mathematics of Operations Research, INFORMS, vol. 39(3), pages 697-711, August.
    9. Steve Alpern & Thomas Lidbetter, 2013. "Mining Coal or Finding Terrorists: The Expanding Search Paradigm," Operations Research, INFORMS, vol. 61(2), pages 265-279, April.
    10. Steve Alpern, 2017. "Hide-and-Seek Games on a Network, Using Combinatorial Search Paths," Operations Research, INFORMS, vol. 65(5), pages 1207-1214, October.
    11. 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.
    12. 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.
    13. Steve Alpern & Vic Baston & Shmuel Gal, 2008. "Network search games with immobile hider, without a designated searcher starting point," International Journal of Game Theory, Springer;Game Theory Society, vol. 37(2), pages 281-302, June.
    14. Shmuel Gal, 2001. "On the optimality of a simple strategy for searching graphs," International Journal of Game Theory, Springer;Game Theory Society, vol. 29(4), pages 533-542.
    15. Reijnierse, J H & Potters, J A M, 1993. "Search Games with Immobile Hider," International Journal of Game Theory, Springer;Game Theory Society, vol. 21(4), pages 385-394.
    16. Jotshi, Arun & Batta, Rajan, 2008. "Search for an immobile entity on a network," European Journal of Operational Research, Elsevier, vol. 191(2), pages 347-359, December.
    17. Donald A. Berry & Roy F. Mensch, 1986. "Discrete Search with Directional Information," Operations Research, INFORMS, vol. 34(3), pages 470-477, June.
    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. Delavernhe, Florian & Jaillet, Patrick & Rossi, André & Sevaux, Marc, 2021. "Planning a multi-sensors search for a moving target considering traveling costs," European Journal of Operational Research, Elsevier, vol. 292(2), pages 469-482.
    2. Benoit Duvocelle & János Flesch & Hui Min Shi & Dries Vermeulen, 2021. "Search for a moving target in a competitive environment," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(2), pages 547-557, June.
    3. Cao, Yiyin & Dang, Chuangyin & Xiao, Zhongdong, 2022. "A differentiable path-following method to compute subgame perfect equilibria in stationary strategies in robust stochastic games and its applications," European Journal of Operational Research, Elsevier, vol. 298(3), pages 1032-1050.
    4. Duvocelle, Benoit & Flesch, János & Staudigl, Mathias & Vermeulen, Dries, 2022. "A competitive search game with a moving target," European Journal of Operational Research, Elsevier, vol. 303(2), pages 945-957.

    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. Duvocelle, Benoit & Flesch, János & Staudigl, Mathias & Vermeulen, Dries, 2022. "A competitive search game with a moving target," European Journal of Operational Research, Elsevier, vol. 303(2), pages 945-957.
    2. Yolmeh, Abdolmajid & Baykal-Gürsoy, Melike, 2021. "Weighted network search games with multiple hidden objects and multiple search teams," European Journal of Operational Research, Elsevier, vol. 289(1), pages 338-349.
    3. Lidbetter, Thomas, 2017. "On the approximation ratio of the Random Chinese Postman Tour for network search," European Journal of Operational Research, Elsevier, vol. 263(3), pages 782-788.
    4. Lidbetter, Thomas, 2020. "Search and rescue in the face of uncertain threats," European Journal of Operational Research, Elsevier, vol. 285(3), pages 1153-1160.
    5. Steve Alpern & Thomas Lidbetter, 2014. "Searching a Variable Speed Network," Mathematics of Operations Research, INFORMS, vol. 39(3), pages 697-711, August.
    6. Steve Alpern & Thomas Lidbetter, 2019. "Approximate solutions for expanding search games on general networks," Annals of Operations Research, Springer, vol. 275(2), pages 259-279, April.
    7. Baston, Vic & Kikuta, Kensaku, 2019. "A search problem on a bipartite network," European Journal of Operational Research, Elsevier, vol. 277(1), pages 227-237.
    8. Steve Alpern, 2011. "Find-and-Fetch Search on a Tree," Operations Research, INFORMS, vol. 59(5), pages 1258-1268, October.
    9. Steve Alpern, 2017. "Hide-and-Seek Games on a Network, Using Combinatorial Search Paths," Operations Research, INFORMS, vol. 65(5), pages 1207-1214, October.
    10. Alpern, Steve & Lidbetter, Thomas, 2020. "Search and Delivery Man Problems: When are depth-first paths optimal?," European Journal of Operational Research, Elsevier, vol. 285(3), pages 965-976.
    11. 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.
    12. Francis Bloch & Bhaskar Dutta & Marcin Dziubi´nski, 2024. "Strategic hiding and exploration in networks," Working Papers 112, Ashoka University, Department of Economics.
    13. 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.
    14. Steve Alpern & Thomas Lidbetter, 2013. "Mining Coal or Finding Terrorists: The Expanding Search Paradigm," Operations Research, INFORMS, vol. 61(2), pages 265-279, April.
    15. 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.
    16. Jotshi, Arun & Batta, Rajan, 2008. "Search for an immobile entity on a network," European Journal of Operational Research, Elsevier, vol. 191(2), pages 347-359, December.
    17. 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.
    18. Bui, Thuy & Lidbetter, Thomas, 2023. "Optimal patrolling strategies for trees and complete networks," European Journal of Operational Research, Elsevier, vol. 311(2), pages 769-776.
    19. 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.
    20. Bastián Bahamondes & Mathieu Dahan, 2024. "Hide-and-Seek Game with Capacitated Locations and Imperfect Detection," Decision Analysis, INFORMS, vol. 21(2), pages 110-124, June.

    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:eee:ejores:v:283:y:2020:i:2:p:783-794. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    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.