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Optimal Expected Rank in a Two-Sided Secretary Problem

Author

Listed:
  • Kimmo Eriksson

    (Department of Mathematics and Physics, Mälardalen University, SE-721 23 Västerås, Sweden)

  • Jonas Sjöstrand

    (Department of Mathematics and Physics, Mälardalen University, SE-721 23 Västerås, Sweden)

  • Pontus Strimling

    (Department of Mathematics and Physics, Mälardalen University, SE-721 23 Västerås, Sweden)

Abstract

In a two-sided version of the famous secretary problem, employers search for a secretary at the same time as secretaries search for an employer. Nobody accepts being put on hold, and nobody is willing to take part in more than N interviews. Preferences are independent, and agents seek to optimize the expected rank of the partner they obtain among the N potential partners. We find that in any subgame perfect equilibrium, the expected rank grows as the square root of N (whereas it tends to a constant in the original secretary problem). We also compute how much agents can gain by cooperation.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:oropre:v:55:y:2007:i:5:p:921-931
    DOI: 10.1287/opre.1070.0403
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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.
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    Cited by:

    1. Alpern, Steve & Gal, Shmuel & Solan, Eilon, 2010. "A sequential selection game with vetoes," Games and Economic Behavior, Elsevier, vol. 68(1), pages 1-14, January.
    2. Alpern, Steve & Katrantzi, Ioanna & Ramsey, David, 2014. "Equilibrium population dynamics when mating is by mutual choice based on age," Theoretical Population Biology, Elsevier, vol. 94(C), pages 63-72.
    3. Kimmo Eriksson & Jonas Sjöstrand & Pontus Strimling, 2008. "Asymmetric equilibria in dynamic two-sided matching markets with independent preferences," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(3), pages 421-440, March.
    4. Alpern, S. & Katrantzi, I. & Ramsey, D.M., 2013. "Partnership formation with age-dependent preferences," European Journal of Operational Research, Elsevier, vol. 225(1), pages 91-99.
    5. Tadeas Priklopil & Krishnendu Chatterjee, 2015. "Evolution of Decisions in Population Games with Sequentially Searching Individuals," Games, MDPI, vol. 6(4), pages 1-25, September.
    6. Longjian Li & Alexis Akira Toda, 2022. "Incentivizing Hidden Types in Secretary Problem," Papers 2208.05897, arXiv.org, revised Jul 2024.
    7. E. M. Parilina & A. Tampieri, 2013. "Marriage Formation with Assortative Meeting as a Two-Sided Optimal Stopping Problem," Working Papers wp886, Dipartimento Scienze Economiche, Universita' di Bologna.
    8. Kimmo Eriksson & Olle Häggström, 2008. "Instability of matchings in decentralized markets with various preference structures," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(3), pages 409-420, March.
    9. Daniel Cownden & David Steinsaltz, 2014. "Effects of Competition in a Secretary Problem," Operations Research, INFORMS, vol. 62(1), pages 104-113, February.
    10. Eriksson, Kimmo & Strimling, Pontus, 2010. "The devil is in the details: Incorrect intuitions in optimal search," Journal of Economic Behavior & Organization, Elsevier, vol. 75(2), pages 338-347, August.
    11. 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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