Restricting Entries to All-Pay Contests
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866912750134886400 |
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| author | Sun, Fupeng Sun, Yanwei Yan, Chiwei Jin, Li |
| author_facet | Sun, Fupeng Sun, Yanwei Yan, Chiwei Jin, Li |
| contents | We study an all-pay contest in which players with low abilities are filtered out before competing for prizes. We consider a setting where the designer admits a certain number of top players. The admitted players update their beliefs based on the signal that their abilities are among the top, which leads to posterior beliefs that, even under i.i.d. priors, are correlated and depend on each player's private ability. We find that all effects of this elimination mechanism -- including the reduction in the number of admitted players and the resulting updated beliefs -- are captured by an \textit{inflated ability}. A symmetric and strictly increasing equilibrium strategy exists if and only if this inflated ability is increasing in the player's true ability. Under this condition, we explicitly characterize the unique strictly increasing Bayesian equilibrium strategy. Focusing on a winner-take-all prize structure, we find that each admitted player's effort strictly decreases as the admitted number increases. As a result, it is optimal to admit only two players in terms of maximizing the expected highest effort. Finally, in a two-stage extension, we find that there does not exist a symmetric and strictly increasing equilibrium strategy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2205_08104 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Restricting Entries to All-Pay Contests Sun, Fupeng Sun, Yanwei Yan, Chiwei Jin, Li Computer Science and Game Theory General Economics Economics We study an all-pay contest in which players with low abilities are filtered out before competing for prizes. We consider a setting where the designer admits a certain number of top players. The admitted players update their beliefs based on the signal that their abilities are among the top, which leads to posterior beliefs that, even under i.i.d. priors, are correlated and depend on each player's private ability. We find that all effects of this elimination mechanism -- including the reduction in the number of admitted players and the resulting updated beliefs -- are captured by an \textit{inflated ability}. A symmetric and strictly increasing equilibrium strategy exists if and only if this inflated ability is increasing in the player's true ability. Under this condition, we explicitly characterize the unique strictly increasing Bayesian equilibrium strategy. Focusing on a winner-take-all prize structure, we find that each admitted player's effort strictly decreases as the admitted number increases. As a result, it is optimal to admit only two players in terms of maximizing the expected highest effort. Finally, in a two-stage extension, we find that there does not exist a symmetric and strictly increasing equilibrium strategy. |
| title | Restricting Entries to All-Pay Contests |
| topic | Computer Science and Game Theory General Economics Economics |
| url | https://arxiv.org/abs/2205.08104 |