Skewing the Odds: Taking Risks for Rank-Based Rewards

Abstract

In competitions for rank-based rewards, how does the structure of rewards affect risk-taking? We answer this question in a framework where, subject only to a mean-performance constraint, contestants compete for rank-based "prizes" by choosing random performance levels. We derive the unique equilibrium of this game and provide a comprehensive analysis of the relation between the equilibrium performance distribution -- including modality, symmetry, tail behavior, dispersion, and skewness -- and the contest structure. Increasing the real gain inequality of prizes, adding contestants, or scaling up contest size increases performance dispersion but not necessarily skewness while convexifying the prize schedule increases both dispersion and skewness.

The supplement to this paper: http://ssrn.com/abstract=2747503

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

JEL Classification: C72, D81, G11