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A new look at the returning secretary problem

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Abstract

We consider a version of the secretary problem in which each candidate has an identical twin. As in the classical secretary problem, the aim is to choose a top candidate, i.e., one of the best twins, with the highest possible probability. We find an optimal stopping rule for such a choice, the probability of success, and its asymptotic behavior. We use a novel technique that allows the problem to be solved exactly in linear time and obtain the asymptotic values by solving differential equations. Furthermore, the proposed technique may be used to study the variants of the same problem and in other optimal stopping problems.

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Authors and Affiliations

  1. Departamento de Matemáticas, Universidad de Oviedo, Avda. Calvo Sotelo s/n, 33007, Oviedo, Spain

    J. M. Grau Ribas

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  1. J. M. Grau Ribas
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Correspondence to J. M. Grau Ribas.

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Ribas, J.M.G. A new look at the returning secretary problem. J Comb Optim 37, 1216–1236 (2019). https://doi.org/10.1007/s10878-018-0349-8

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  • DOI: https://doi.org/10.1007/s10878-018-0349-8

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