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A generalized secretary problem

Author

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  • Abba M. Krieger
  • Ester Samuel-Cahn

Abstract

A new Secretary Problem is considered, where for fixed k and m one wins if at some time i = m(j .. 1) + 1 up to jm one selects one of the j best items among the first jm items, j = 1,...,k. Selection is based on relative ranks only. Interest lies in small k values, such as k = 2 or 3. This is compared with the classical rule, where one wins if one of the k best among the n = km items is chosen. We prove that the win probability in the new formulation is always larger than in the classical one. We also show, for k = 2 and 3 that one stops sooner in the new formulation. Numerical comparisons are included.

Suggested Citation

  • Abba M. Krieger & Ester Samuel-Cahn, 2014. "A generalized secretary problem," Discussion Paper Series dp668, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    • Handle: RePEc:huj:dispap:dp668
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    File URL: http://ratio.huji.ac.il/sites/default/files/publications/dp668.pdf
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    References listed on IDEAS

    as
    1. Frank, Arthur Q. & Samuels, Stephen M., 1980. "On an optimal stopping problem of Gusein-Zade," Stochastic Processes and their Applications, Elsevier, vol. 10(3), pages 299-311, October.
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