IDEAS home Printed from https://ideas.repec.org/a/spr/mathme/v60y2004i3p437-451.html
   My bibliography  Save this article

A non-zero-sum no-information best-choice game

Author

Listed:
  • Minoru Sakaguchi
  • Vladimir V. Mazalov

Abstract

A given number of n applicants are to be interviewed for a position of secretary. They present themselves one-by-one in random order, all n! permutations being equally likely. Two players I and II jointly interview the i-th applicant and observe that his (or her) relative rank is y for I and z for II, relative to i−1 applicants that have already seen (rank 1 is for the best). Each player chooses one of the two choices Accept or Reject. If choice-pair is R-R, then the i-th is rejected, and the players face the next i+1-th applicant. If A-A is chosen, then the game ends with payoff to I (II), the expected absolute rank under the condition that the i-th has the relative rank y (z). If players choose different choices, then arbitration comes in, and forces players to take the same choices as I’s (II’s) with probability [InlineMediaObject not available: see fulltext.] Arbitration is fair if p=1/2. If all applicants except the last have been rejected, then A-A should be chosen for the last. Each player aims to minimize the expected payoff he can get. Explicit solution is derived to this n stage game, and numerical results are given for some n and p. The possibility of an interactive approach in this selection problem is analyzed. Copyright Springer-Verlag 2004

Suggested Citation

  • Minoru Sakaguchi & Vladimir V. Mazalov, 2004. "A non-zero-sum no-information best-choice game," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 60(3), pages 437-451, December.
  • Handle: RePEc:spr:mathme:v:60:y:2004:i:3:p:437-451
    DOI: 10.1007/s001860400366
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s001860400366
    Download Restriction: Access to full text is restricted to subscribers.

    File URL: https://libkey.io/10.1007/s001860400366?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.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Rohan DUTTA, 2016. "Joint Search with No Information: An Inefficient Immediate Agreement Theorem," Cahiers de recherche 12-2016, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    2. Vincent Mak & Darryl A. Seale & Amnon Rapoport & Eyran J. Gisches, 2019. "Voting Rules in Sequential Search by Committees: Theory and Experiments," Management Science, INFORMS, vol. 65(9), pages 4349-4364, September.
    3. Fouad Abdelaziz & Saoussen Krichen, 2007. "Optimal stopping problems by two or more decision makers: a survey," Computational Management Science, Springer, vol. 4(2), pages 89-111, April.
    4. Vladimir V. Mazalov & Anna A. Ivashko & Elena N. Konovalchikova, 2016. "Optimal Strategies in Best-Choice Game with Incomplete Information — The Voice Show," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 18(02), pages 1-18, June.
    5. Mak, Vincent & Rapoport, Amnon & Seale, Darryl A., 2014. "Sequential search by groups with rank-dependent payoffs: An experimental study," Organizational Behavior and Human Decision Processes, Elsevier, vol. 124(2), pages 256-267.
    6. Dutta, Rohan, 2017. "Joint search with no information: An immediate agreement theorem," Economics Letters, Elsevier, vol. 160(C), pages 43-45.
    7. David M. Ramsey, 2020. "A Game Theoretic Model of Choosing a Valuable Good via a Short List Heuristic," Mathematics, MDPI, vol. 8(2), pages 1-20, February.

    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:spr:mathme:v:60:y:2004:i:3:p:437-451. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.