Approximate Results for a Generalized Secretary Problem

Chris Dietz, Dinard van der Laan and Ad Ridder
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Chris Dietz: VU University Amsterdam
Dinard van der Laan: VU University Amsterdam
Ad Ridder: VU University Amsterdam

No 10-092/4, Tinbergen Institute Discussion Papers from Tinbergen Institute

Abstract: This discussion paper resulted in a publication in 'Probability in the Engineering and Informational Sciences' , 2011, 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.

Keywords: Secretary Problem; Dynamic Programming; Approximate Policies (search for similar items in EconPapers)
JEL-codes: C60 C61 (search for similar items in EconPapers)
Date: 2010-09-10
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