Incentivizing Hidden Types in Secretary Problem
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866918087734853632 |
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| author | Li, Longjian Toda, Alexis Akira |
| author_facet | Li, Longjian Toda, Alexis Akira |
| contents | 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 $N^{-c}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_05897 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Incentivizing Hidden Types in Secretary Problem Li, Longjian Toda, Alexis Akira Theoretical Economics Computer Science and Game Theory Optimization and Control 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 $N^{-c}$. |
| title | Incentivizing Hidden Types in Secretary Problem |
| topic | Theoretical Economics Computer Science and Game Theory Optimization and Control |
| url | https://arxiv.org/abs/2208.05897 |