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arXiv · 2009.07911

The multi-returning secretary problem

L. Bayon·P. Fortuny·J. M. Grau·A. Oller Marcen·M. M. Ruiz
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Abstract

In this paper we consider the so-called Multi-returning secretary problem, a version of the Secretary problem in which each candidate has $m$ identical copies. The case $m=2$ has already been completely solved by several authors using different methods both the case $m>2$ had not been satisfactorily solved yet. Here, we provide and efficient algorithm to compute the optimal threshold and the probability of success for every $m$. Moreover, we give a method to determine their asymtoptic values based on the solution of a system of $m$ ODEs.

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L. Bayon, P. Fortuny, J. M. Grau, A. Oller Marcen, M. M. Ruiz. 2020-09-16. The multi-returning secretary problem. https://arxiv.org/abs/2009.07911

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