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Rendezvous-Evasion Search in Two Boxes

Author

Listed:
  • S. Gal

    (Department of Statistics, University of Haifa, Haifa 31905, Israel)

  • J. V. Howard

    (Department of Statistics, London School of Economics, Houghton Street, London WC2A 2AE, United Kingdom)

Abstract

An agent (who may or may not want to be found) is located in one of two boxes. At time 0 suppose that he is in box B . With probability p he wishes to be found, in which case he has been asked to stay in box B . With probability 1−p he tries to evade the searcher, in which case he may move between boxes A and B . The searcher looks into one of the boxes at times 1, 2, 3, … . Between each search the agent may change boxes if he wants. The searcher is trying to minimise the expected time to discovery. The agent is trying to minimise this time if he wants to be found, but trying to maximise it otherwise. This paper finds a solution to this game (in a sense defined in the paper), associated strategies for the searcher and each type of agent, and a continuous value function v(p) giving the expected time for the agent to be discovered. The solution method (which is to solve an associated zero-sum game) would apply generally to this type of game of incomplete information.

Suggested Citation

  • S. Gal & J. V. Howard, 2005. "Rendezvous-Evasion Search in Two Boxes," Operations Research, INFORMS, vol. 53(4), pages 689-697, August.
    • Handle: RePEc:inm:oropre:v:53:y:2005:i:4:p:689-697
    DOI: 10.1287/opre.1040.0198
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    References listed on IDEAS

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    1. Steve Alpern & Shmuel Gal, 2002. "Searching for an Agent Who May OR May Not Want to be Found," Operations Research, INFORMS, vol. 50(2), pages 311-323, April.
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    Cited by:

    1. Dinah Rosenberg & Eilon Solan & Nicolas Vieille, 2009. "Protocols with No Acknowledgment," Operations Research, INFORMS, vol. 57(4), pages 905-915, August.
    2. Leone, Pierre & Buwaya, Julia & Alpern, Steve, 2022. "Search-and-rescue rendezvous," European Journal of Operational Research, Elsevier, vol. 297(2), pages 579-591.
    3. Steve Alpern & Thomas Lidbetter, 2013. "Mining Coal or Finding Terrorists: The Expanding Search Paradigm," Operations Research, INFORMS, vol. 61(2), pages 265-279, April.
    4. Pierre Leone & Steve Alpern, 2018. "Rendezvous search with markers that can be dropped at chosen times," Naval Research Logistics (NRL), John Wiley & Sons, vol. 65(6-7), pages 449-461, September.
    5. Steven M. Shechter & Farhad Ghassemi & Yasin Gocgun & Martin L. Puterman, 2015. "Technical Note—Trading Off Quick versus Slow Actions in Optimal Search," Operations Research, INFORMS, vol. 63(2), pages 353-362, April.

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