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Effects of Competition in a Secretary Problem

Author

Listed:
  • Daniel Cownden

    (School of Biology, University of St Andrews, St Andrews KY16 9TS, United Kingdom)

  • David Steinsaltz

    (Department of Statistics, University of Oxford, Oxford OX1 3TG, United Kingdom)

Abstract

In a novel multiplayer extension of the famous secretary problem, multiple players seek to employ secretaries from a common labour pool. Secretaries do not accept being put on hold, always accept job offers immediately, and leave the labour pool once rejected by a single player. All players have an identical preference for secretaries, and all players seek to optimize the probability of obtaining the best of all n secretaries. We find that in the Nash equilibrium, as the number, N , of players searching the labour pool grows, the optimal strategy converges to a simple function of N . For the two-player case we also compute how much players can gain through cooperation and how the optimal strategy changes under a payoff structure that promotes spite.

Suggested Citation

  • Daniel Cownden & David Steinsaltz, 2014. "Effects of Competition in a Secretary Problem," Operations Research, INFORMS, vol. 62(1), pages 104-113, February.
    • Handle: RePEc:inm:oropre:v:62:y:2014:i:1:p:104-113
    DOI: 10.1287/opre.2013.1233
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    References listed on IDEAS

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    1. D. V. Lindley, 1961. "Dynamic Programming and Decision Theory," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 10(1), pages 39-51, March.
    2. Kimmo Eriksson & Jonas Sjöstrand & Pontus Strimling, 2007. "Optimal Expected Rank in a Two-Sided Secretary Problem," Operations Research, INFORMS, vol. 55(5), pages 921-931, October.
    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.
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    Cited by:

    1. Steve Alpern & Vic Baston, 2017. "The Secretary Problem with a Selection Committee: Do Conformist Committees Hire Better Secretaries?," Management Science, INFORMS, vol. 63(4), pages 1184-1197, April.

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