DP17107 Tournaments with Reserve Performance
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.