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Mathematics > Probability

arXiv:1009.0626 (math)
[Submitted on 3 Sep 2010]

Title:Approximate results for a generalized secretary problem

Authors:Chris Dietz, Dinard van der Laan, Ad Ridder
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Abstract: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 a preassigned (natural) 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 tends to infinity) results, which show that the double-level policy is an extremely accurate approximation.
Comments: 15 pages, 2 figures
Subjects: Probability (math.PR); Computer Science and Game Theory (cs.GT)
MSC classes: 60C05, 90C39
Cite as: arXiv:1009.0626 [math.PR]
  (or arXiv:1009.0626v1 [math.PR] for this version)
  https://doi.org/10.48550/arXiv.1009.0626

Submission history

From: Ad Ridder [view email]
[v1] Fri, 3 Sep 2010 10:27:45 UTC (15 KB)
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