2010/09/03 by Dietz, Chris, van der Laan, Dinard, Ridder, Ad
#60C05 #90C39 #Computer Science and Game Theory (cs.GT) #FOS: Computer and information sciences #FOS: Mathematics #Probability (math.PR)
paper · doi:10.48550/arxiv.1009.0626
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.