Contest Design with Threshold Objectives

TL;DR

This paper explores contest designs with threshold-based objectives, focusing on maximizing utility when players' outputs are within certain ranges, and characterizes optimal contests for these objectives.

Contribution

It introduces and analyzes two new contest objectives based on thresholds, providing characterizations of optimal contests and computational techniques.

Findings

Optimal contests are characterized for both binary and linear threshold objectives.

Techniques for efficiently computing the optimal contests are provided.

The study extends the understanding of contest design beyond total output maximization.

Abstract

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.