Many sales, sports, and research contests are put in place to maximize contestants’ performance. We investigate and provide a complete characterization of the prize structures that achieve this objective in settings with many contestants. The contestants may be ex ante asymmetric in their abilities and prize valuations, and there may be complete or incomplete information about these parameters. The prize valuations and performance costs may be linear, concave, or convex. A main novel takeaway is that awarding numerous different prizes whose values gradually decline with contestants’ ranking is optimal in the typical case of contestants with convex performance costs and concave prize valuations. This suggests that many real-world contests can be improved by increasing the number of prizes and making them more heterogeneous. The techniques we develop can also be used to formulate and solve other contest design questions that have so far proven intractable.

中文翻译：

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性能最大化的大型竞赛

举办了许多销售、体育和研究竞赛，以最大限度地提高参赛者的表现。我们调查并提供了在有许多参赛者的环境中实现这一目标的奖品结构的完整特征。参赛者在他们的能力和奖品估价方面可能事前不对称，并且关于这些参数可能存在完整或不完整的信息。奖品估值和绩效成本可以是线性的、凹的或凸的。一个主要的新颖观点是，在典型的参赛者表现成本凸出而奖品估值凹入的情况下，颁发价值随着参赛者排名而逐渐下降的众多不同奖项是最佳的。这表明可以通过增加奖品数量并使其更加多样化来改善许多现实世界的比赛。