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arXiv · 1508.07931

A Secretary Problem with a Sliding Window for Recalling Applicants

Shan-Yuan Ho·Abijith Krishnan
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Abstract

The Sliding Window Secretary Problem allows a window of choices to the Classical Secretary Problem, in which there is the option to choose the previous $K$ choices immediately prior to the current choice. We consider a case of this sequential choice problem in which the interviewer has a finite, known number of choices and can only discern the relative ranks of choices, and in which every permutation of ranks is equally likely. We examine three cases of the problem: (i) the interviewer has one choice to choose the best applicant; (ii) the interviewer has one choice to choose one of the top two applicants; and (iii) the interviewer has two choices to choose the best applicant. The form of the optimal strategy is shown, the probability of winning as a function of the window size is derived, and the limiting behavior is discussed for all three cases.

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Shan-Yuan Ho, Abijith Krishnan. 2015-08-31. A Secretary Problem with a Sliding Window for Recalling Applicants. https://arxiv.org/abs/1508.07931

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