Contest Design with Threshold Objectives

We study contests where the designer's objective is an extension of the widely studied objective of maximizing the total output: The designer gets zero marginal utility from a player's output if the output of the player is very low or very high. We consider two variants of this setting, which correspond to two objective functions: binary threshold, where the designer's utility is a non-decreasing function of the number of players with output above a certain threshold; and linear threshold, where a player's contribution to the designer's utility is linear in her output if the output is between a lower and an upper threshold, and becomes constant below the lower and above the upper threshold. For both of these objectives, we study rank-order allocation contests and general contests. We characterize the contests that maximize the designer's objective and indicate techniques to efficiently compute them.