A Double Secretary Problem
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866914160963485696 |
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| author | Hsiau, Shoou-Ren Lin, Yi-Shen |
| author_facet | Hsiau, Shoou-Ren Lin, Yi-Shen |
| contents | We consider a double secretary problem which contains $2n$ applicants of $n$ different qualities, two of each quality. As in the classical secretary problem (CSP), the applicants are interviewed sequentially in a random order by a manager and the manager wants to find an optimal stopping rule that maximizes the probability of selecting one of the two best applicants. We prove that the problem leads to a monotone structure and so the corresponding one-stage look-ahead rule (which is of threshold type) is optimal. The limiting behavior of the rule and of the maximum probability are studied and compared with that of the CSP. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_07201 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Double Secretary Problem Hsiau, Shoou-Ren Lin, Yi-Shen Probability 60G40, 62L15 We consider a double secretary problem which contains $2n$ applicants of $n$ different qualities, two of each quality. As in the classical secretary problem (CSP), the applicants are interviewed sequentially in a random order by a manager and the manager wants to find an optimal stopping rule that maximizes the probability of selecting one of the two best applicants. We prove that the problem leads to a monotone structure and so the corresponding one-stage look-ahead rule (which is of threshold type) is optimal. The limiting behavior of the rule and of the maximum probability are studied and compared with that of the CSP. |
| title | A Double Secretary Problem |
| topic | Probability 60G40, 62L15 |
| url | https://arxiv.org/abs/2511.07201 |