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arXiv · 2208.05897

Incentivizing Hidden Types in Secretary Problem

Longjian Li·Alexis Akira Toda
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Abstract

We study a game between $N$ job applicants who incur a cost $c$ (relative to the job value) to reveal their type during interviews and an administrator who seeks to maximize the probability of hiring the best. We define a full learning equilibrium and prove its existence, uniqueness, and optimality. In equilibrium, the administrator accepts the current best applicant $n$ with probability $c$ if $n<n^*$ and with probability 1 if $n\ge n^*$ for a threshold $n^*$ independent of $c$. In contrast to the case without cost, where the success probability converges to $1/\mathrm{e}\approx 0.37$ as $N$ tends to infinity, with cost the success probability decays like $N^{-c}$.

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BibTeXRIS

Longjian Li, Alexis Akira Toda. 2022-08-11. Incentivizing Hidden Types in Secretary Problem. https://doi.org/10.1007/s00182-025-00922-w

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