When Should You Stop and what do You Get? Some Secretary Problems

Ester Samuel-Cahn

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

Abstract: A version of a secretary problem is considered: Let X j , j = 1,...,n be i.i.d. random variables. Like in the classical secretary problem the optimal stopper only observes Y j = 1, if X j is a (relative) record, and Y j = 0, otherwise. The actual X j -values are not revealed. The goal is to maximize the expected X-value at which one stops. We describe the structure of the optimal stopping rule, its asymptotic properties and the asymptotic expected reward. Three different families of distributions of X are considered, belonging to the three different domains of attraction of the maximum. It is shown that both the time of stopping, as well as the expected reward are strongly distribution dependent. The last section discusses an ‘inverse’ of ‘Robbins’ Problem’.

Keywords: domain of attraction; relative record; relative rank; Secretary Problem; stopping rule; stopping value (search for similar items in EconPapers)
Pages: 11 pages
Date: 2005-10
References: View complete reference list from CitEc
Citations:

Forthcoming in Sequential Analysis.

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