A generalized secretary problem

Abba M. Krieger and Ester Samuel-Cahn

Discussion Paper Series from The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem

Abstract: A new Secretary Problem is considered, where for fixed k and m one wins if at some time i = m(j .. 1) + 1 up to jm one selects one of the j best items among the first jm items, j = 1,...,k. Selection is based on relative ranks only. Interest lies in small k values, such as k = 2 or 3. This is compared with the classical rule, where one wins if one of the k best among the n = km items is chosen. We prove that the win probability in the new formulation is always larger than in the classical one. We also show, for k = 2 and 3 that one stops sooner in the new formulation. Numerical comparisons are included.

Keywords: Secretary Problem; Optimal Stopping Rule; Time Dependent Win Probability; Relative Rank (search for similar items in EconPapers)
Pages: 22 pages
Date: 2014-07
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