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PreprintCC BY-NC-ND 4.0arXiv

Strategic Interview Positioning under Uncertain Self-Rank

  • Jose Á. Islas
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Abstract

We study interview positioning in the secretary problem when an applicant is uncertain about their own absolute rank. The employer uses a given rejection threshold, and the applicant's self-rank distribution is truncated geometric. We show that the applicant need only compare the first eligible position with the final position and that, for finite n, a unique critical value exists precisely when r(r+1)>n−1. If rn is the employer's rejection threshold and rn/n→α∈(0,1) as n→∞, then limn→∞qc(n,rn) = qc(α) = (1−α)/(1−α+α2). Thus uncertainty about absolute rank produces an explicit asymptotic phase transition in optimal interview positioning.

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Cite

BibTeXRIS
BibTeX
@misc{islas2026strategic,
  title = {{Strategic Interview Positioning under Uncertain Self-Rank}},
  author = {Jose Á. Islas},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2609.11826},
  eprint = {2609.11826},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.11826},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - Strategic Interview Positioning under Uncertain Self-Rank
AU  - Jose Á. Islas
PY  - 2026
DA  - 2026/10/01
PB  - arXiv
DO  - 10.48550/arxiv.2609.11826
UR  - https://arxiv.org/abs/2609.11826
AB  - We study interview positioning in the secretary problem when an applicant is uncertain about their own absolute rank. The employer uses a given rejection threshold, and the applicant's self-rank distribution is truncated geometric. We show that the applicant need only compare the first eligible position with the final position and that, for finite n, a unique critical value exists precisely when r(r+1)>n−1. If r_n is the employer's rejection threshold and r_n/n→α∈(0,1) as n→∞, then lim_n→∞q_c(n,r_n) = q_c(α) = (1−α)/(1−α+α^2). Thus uncertainty about absolute rank produces an explicit asymptotic phase transition in optimal interview positioning.
ER  -