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Robust Tournaments

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  • Mikhail Drugov
  • Dmitry Ryvkin

Abstract

We characterize robust tournament design -- the prize scheme that maximizes the lowest effort in a rank-order tournament where the distribution of noise is unknown, except for an upper bound, $\bar{H}$, on its Shannon entropy. The robust tournament scheme awards positive prizes to all ranks except the last, with a distinct top prize. Asymptotically, the prizes follow the harmonic number sequence and induce an exponential distribution of noise with rate parameter $e^{-\bar{H}}$. The robust prize scheme is highly unequal, especially in small tournaments, but becomes more equitable as the number of participants grows, with the Gini coefficient approaching $1/2$.

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  • Mikhail Drugov & Dmitry Ryvkin, 2025. "Robust Tournaments," Papers 2507.16348, arXiv.org.
    • Handle: RePEc:arx:papers:2507.16348
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    File URL: http://arxiv.org/pdf/2507.16348
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