Template-Type: ReDIF-Paper 1.0 Series: Tinbergen Institute Discussion Papers Creation-Date: 2010-09-10 Number: 10-092/4 Author-Name: Chris Dietz Author-Workplace-Name: VU University Amsterdam Author-Name: Dinard van der Laan Author-Workplace-Name: VU University Amsterdam Author-Name: Ad Ridder Author-Workplace-Name: VU University Amsterdam Title: Approximate Results for a Generalized Secretary Problem 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. Classification-JEL: C60, C61 Keywords: Secretary Problem, Dynamic Programming, Approximate Policies File-Url: http://papers.tinbergen.nl/10092.pdf File-Format: application/pdf File-Size: 194588 bytes Handle: RePEc:tin:wpaper:20100092