In winner-take-all tournaments, agents’ performance is determined jointly by effort and luck, and the top performer is rewarded. We study the impact of the “shape of luck”—the details of the distribution of performance shocks—on incentives in such settings. We are concerned with the effects of increasing the number of competitors, which can be deterministic or stochastic, on individual and aggregate effort. We show that these effects are determined by the shape of the density and failure (hazard) rate of the distribution of shocks. When shocks have heavy tails, aggregate effort can decrease in the number of competitors.

中文翻译：

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赢家通吃锦标赛中运气和竞争的形态

在赢家通吃的比赛中，代理人的表现由努力和运气共同决定，表现最好的人得到奖励。我们研究了“运气的形状”——绩效冲击分布的细节——在这种情况下对激励的影响。我们关注增加竞争者数量对个人和总体努力的影响，这可能是确定性的或随机的。我们表明，这些影响是由冲击分布的密度和失效（危险）率的形状决定的。当冲击有重尾时，总的努力会减少竞争者的数量。