Incentive Effects of a Cut-Off Score: Optimal Contest Design with Transparent Pre-Selection

TL;DR

This paper analyzes how transparent cut-off scores in shortlisting influence contestant behavior and contest outcomes, revealing optimal contest formats and the impact of shortlisting on performance metrics.

Contribution

It provides a full characterization of equilibrium behaviors in rank-order contests with shortlisting and identifies optimal contest structures under different objectives.

Findings

Optimal contest is winner-take-all for both objectives.

Shortlist size of two maximizes individual performance.

Performance with shortlisting exceeds that without by 4/3.

Abstract

Shortlisting is a common and effective method for pre-selecting participants in competitive settings. To ensure fairness, a cut-off score is typically announced, allowing only contestants who exceed it to enter the contest, while others are eliminated. In this paper, we study rank-order contests with shortlisting and cut-off score disclosure. We fully characterize the equilibrium behavior of shortlisted contestants for any given prize structure and shortlist size. We examine two objective functions: the highest individual performance and total performance. For both objectives, the optimal contest is in a winner-take-all format. For the highest individual performance, the optimal shortlist size is exactly two contestants, but, in contrast, for total performance, the shortlist size does not affect the outcome, i.e., any size yields the same total performance. Furthermore, we compare the highest individual performance achieved with and without shortlisting, and show that the former is 4/3 times greater than the latter.