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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
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    Citations

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    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.

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