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Approximate Results for a Generalized Secretary Problem


Author Info

  • Chris Dietz

    (VU University Amsterdam)

  • Dinard van der Laan

    (VU University Amsterdam)

  • Ad Ridder

    (VU University Amsterdam)


This discussion paper resulted in a publication in 'Probability in the Engineering and Informational Sciences' , 25(2), 157-69. A version of the classical secretary problem is studied, in which one is interested in selecting one of the b best out of a group of n differently ranked persons who are presented one by one in a random order. It is assumed that b is bigger than or equal to 1 is a preassigned number. It is known, already for a long time, that for the optimal policy one needs to compute b position thresholds, for instance via backwards induction. In this paper we study approximate policies, that use just a single or a double position threshold, albeit in conjunction with a level rank. We give exact and asymptotic (as n goes to infinity) results, which show that the double-level policy is an extremely accurate approximation.

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Bibliographic Info

Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 10-092/4.

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Date of creation: 10 Sep 2010
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Handle: RePEc:dgr:uvatin:20100092

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Keywords: Secretary Problem; Dynamic Programming; Approximate Policies;

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