Working Paper: CEPR ID: DP17107
Authors: Mikhail Drugov; Dmitry Ryvkin; Jun Zhang
Abstract: We study tournaments where winning a rank-dependent prize requires passing a reserve - a minimum performance standard. Agents' performance is determined by effort and noise. For log-concave noise distributions the optimal reserve is at the modal performance, and the optimal prize scheme is winner-take-all. In contrast, for log-convex noise distributions the optimal reserve is at the lower bound of the distribution of performance, which is passed with probability one in equilibrium, and it is optimal to award equal prizes to all qualifying agents. These pay schemes are optimal in a general class of symmetric monotone contracts that may depend on cardinal performance.
Keywords: tournament; reserve performance; prize sharing
JEL Codes: C72; D72; D82
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| reserve performance (Q21) | player effort (Z22) |
| log-concave distribution (C46) | optimal reserve at modal performance (E63) |
| log-convex distribution (C46) | optimal reserve at lower bound (C61) |
| reserve performance (Q21) | prize allocation schemes (D44) |
| noise distribution characteristics (C46) | optimal tournament designs (C72) |
| light-tailed noise distributions (C46) | higher expected performance (D29) |
| heavy-tailed distributions (C46) | individual bonuses instead of competitive prizes (J33) |