How do prize structures affect contestant risk-taking strategies in contests? We address this question using a model where, subject only to a capacity constraint on mean performance, an arbitrary number of contestants compete for rankbased prizes through choosing random performance levels. Based on the closed-form solution of the unique equilibrium, we examine the relation between the prize structure and the shape of the equilibrium performance distribution, including (a)symmetry, modality, and tail behavior, and study the factors that affect performance dispersion and skewness. Increasing real gain inequality, adding contestants, and merging contests all make performance more dispersed but not necessarily more right-skewed. In contrast, convexifying prize schedule increases both performance dispersion and rightskewness, implying that the common heuristics for rank-based prize allocations used in economics, such as the power law and Gibrat’s law, always imply highly dispersed and right-skewed contestant performance. (JEL C72, D81, G11)

Keywords: contests, risk taking, dispersion, skewness, prize inequality