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.
Highlights
The classical secretary problem (CSP) has been extensively studied in the literature on optimal stopping
The CSP the natural question arises: what is the optimal strategy if one of the assumptions will change? Most of the articles focus on changing the fifth condition of the CSP
In many experiments connected with the CSP, it has been noticed that the decision maker (DM) do not hold the best strategy derived from the mathematical models
Summary
The classical secretary problem (CSP) has been extensively studied in the literature on optimal stopping. Its origins can be found in the middle of the 20th century (see Ferguson [1]). The original statement of the problem is as follows: 2. There is a fixed and known number of applicants for a position. The applicants are interviewed sequentially in random order. The DM has a binary payoff: 1 for selecting the best applican in the whole group and 0 otherwise. He can stop only once during the search. The solution of CSP is well known. The original model has been extended in several directions
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