IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v145y2022icp226-240.html
   My bibliography  Save this article

The best choice problem with random arrivals: How to beat the 1/e-strategy

Author

Listed:
  • Gnedin, Alexander

Abstract

In the best choice problem with random arrivals, an unknown number n of rankable items arrive at times sampled from the uniform distribution. As is well known, a real-time player can ensure stopping at the overall best item with probability at least 1/e, by waiting until time 1/e then selecting the first relatively best item (record) to appear, if available. This paper discusses the issue of dominance in a wide class of multi-cutoff stopping strategies of best choice, and argues that in fact the player faces a trade-off between success probabilities for various values of n. We show that the 1/e-strategy is not a unique minimax strategy and that it can be improved in various ways.

Suggested Citation

  • Gnedin, Alexander, 2022. "The best choice problem with random arrivals: How to beat the 1/e-strategy," Stochastic Processes and their Applications, Elsevier, vol. 145(C), pages 226-240.
    • Handle: RePEc:eee:spapps:v:145:y:2022:i:c:p:226-240
    DOI: 10.1016/j.spa.2021.12.008
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414921002118
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2021.12.008?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. Mitsushi Tamaki & Qi Wang, 2010. "A Random Arrival Time Best-Choice Problem with Uniform Prior on the Number of Arrivals," Springer Optimization and Its Applications, in: Altannar Chinchuluun & Panos M. Pardalos & Rentsen Enkhbat & Ider Tseveendorj (ed.), Optimization and Optimal Control, pages 499-510, Springer.
    2. Bruss, F. Thomas, 1988. "Invariant record processes and applications to best choice modelling," Stochastic Processes and their Applications, Elsevier, vol. 30(2), pages 303-316, December.
    3. Browne, Sid & Bunge, John, 1995. "Random record processes and state dependent thinning," Stochastic Processes and their Applications, Elsevier, vol. 55(1), pages 131-142, January.
    4. Bruss, F. Thomas & Rogers, L. C. G., 1991. "Embedding optimal selection problems in a Poisson process," Stochastic Processes and their Applications, Elsevier, vol. 38(2), pages 267-278, August.
    5. T. J. Stewart, 1981. "The Secretary Problem with an Unknown Number of Options," Operations Research, INFORMS, vol. 29(1), pages 130-145, February.
    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. Alexander Gnedin & Zakaria Derbazi, 2022. "Trapping the Ultimate Success," Mathematics, MDPI, vol. 10(1), pages 1-19, January.
    2. Bruss, F. Thomas & Rogers, L.C.G., 2022. "The 1/e-strategy is sub-optimal for the problem of best choice under no information," Stochastic Processes and their Applications, Elsevier, vol. 150(C), pages 1059-1067.
    3. Kühne, Robert & Rüschendorf, Ludger, 2000. "Approximation of optimal stopping problems," Stochastic Processes and their Applications, Elsevier, vol. 90(2), pages 301-325, December.
    4. Bruss, F. Thomas & Paindaveine, Davy, 2000. "Selecting a sequence of last successes in independent trials," MPRA Paper 21166, University Library of Munich, Germany.
    5. Das, Sanmay & Tsitsiklis, John N., 2010. "When is it important to know you've been rejected? A search problem with probabilistic appearance of offers," Journal of Economic Behavior & Organization, Elsevier, vol. 74(1-2), pages 104-122, May.
    6. Anton J. Kleywegt & Jason D. Papastavrou, 1998. "The Dynamic and Stochastic Knapsack Problem," Operations Research, INFORMS, vol. 46(1), pages 17-35, February.
    7. Anton J. Kleywegt & Jason D. Papastavrou, 2001. "The Dynamic and Stochastic Knapsack Problem with Random Sized Items," Operations Research, INFORMS, vol. 49(1), pages 26-41, February.
    8. Ferenstein, Elzbieta Z. & Krasnosielska, Anna, 2010. "No-information secretary problems with cardinal payoffs and Poisson arrivals," Statistics & Probability Letters, Elsevier, vol. 80(3-4), pages 221-227, February.
    9. Tomomi Matsui & Katsunori Ano, 2016. "Lower Bounds for Bruss’ Odds Problem with Multiple Stoppings," Mathematics of Operations Research, INFORMS, vol. 41(2), pages 700-714, May.
    10. Seale, Darryl A. & Rapoport, Amnon, 1997. "Sequential Decision Making with Relative Ranks: An Experimental Investigation of the "Secretary Problem">," Organizational Behavior and Human Decision Processes, Elsevier, vol. 69(3), pages 221-236, March.
    11. Gnedin, A.V.Alexander V., 2004. "Best choice from the planar Poisson process," Stochastic Processes and their Applications, Elsevier, vol. 111(2), pages 317-354, 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:spapps:v:145:y:2022:i:c:p:226-240. 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/wps/find/journaldescription.cws_home/505572/description#description .

    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.