Tournaments with a Standard
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916502584688640 |
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| author | Drugov, Mikhail Ryvkin, Dmitry Zhang, Jun |
| author_facet | Drugov, Mikhail Ryvkin, Dmitry Zhang, Jun |
| contents | We study tournaments where winning a rank-dependent prize requires passing a minimum performance standard. We show that, for any prize allocation, the optimal standard is always at a mode of performance that is weakly higher than the global mode and identify a necessary and sufficient condition for it to be at the global mode. When the prize scheme can be designed as well, the winner-take-all prize scheme is optimal for noise distributions with an increasing failure rate; and awarding equal prizes to all qualifying agents is optimal for noise distributions with a decreasing failure rate. For distributions with monotone likelihood ratios -- log-concave and log-convex, respectively -- these pay schemes are also optimal in a larger class of anonymous, monotone contracts that may depend on cardinal performance. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_01139 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Tournaments with a Standard Drugov, Mikhail Ryvkin, Dmitry Zhang, Jun Theoretical Economics We study tournaments where winning a rank-dependent prize requires passing a minimum performance standard. We show that, for any prize allocation, the optimal standard is always at a mode of performance that is weakly higher than the global mode and identify a necessary and sufficient condition for it to be at the global mode. When the prize scheme can be designed as well, the winner-take-all prize scheme is optimal for noise distributions with an increasing failure rate; and awarding equal prizes to all qualifying agents is optimal for noise distributions with a decreasing failure rate. For distributions with monotone likelihood ratios -- log-concave and log-convex, respectively -- these pay schemes are also optimal in a larger class of anonymous, monotone contracts that may depend on cardinal performance. |
| title | Tournaments with a Standard |
| topic | Theoretical Economics |
| url | https://arxiv.org/abs/2412.01139 |