Secretary Problem with Possible Errors in Observation

Marek Skarupski
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Marek Skarupski: Faculty of Pure and Applied Mathematics, Wrocław University of Science and Technology, Wyb. Wyspianskiego 27, 50-370 Wrocław, Poland

Mathematics, 2020, vol. 8, issue 10, 1-10

Abstract: The classical secretary problem models a situation in which the decision maker can select or reject in the sequential observation objects numbered by the relative ranks. In theoretical studies, it is known that the strategy is to reject the first 37% of objects and select the next relative best one. However, an empirical result for the problem is that people do not apply the optimal rule. In this article, we propose modeling doubts of decision maker by considering a modification of the secretary problem. We assume that the decision maker can not observe the relative ranks in a proper way. We calculate the optimal strategy in such a problem and the value of the problem. In special cases, we also combine this problem with the no-information best choice problem and a no-information second-best choice problem.

Keywords: secretary problem; threshold rule; optimal stopping; no-information case (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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