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Tournaments with a Standard

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  • Mikhail Drugov
  • Dmitry Ryvkin
  • Jun Zhang

Abstract

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.

Suggested Citation

  • Mikhail Drugov & Dmitry Ryvkin & Jun Zhang, 2024. "Tournaments with a Standard," Papers 2412.01139, arXiv.org.
    • Handle: RePEc:arx:papers:2412.01139
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    File URL: http://arxiv.org/pdf/2412.01139
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