Optimal Grading: A Unified Approach

2026-08-24

AI Summary

研究提出一种统一方法，通过调整奖励分配来最大化全支付竞赛中的预期总努力，适用于基于排名和基于表现的评分制度。

Abstract

We develop a unified approach to optimal grading in an all-pay contest in which a designer assigns a fixed vector of heterogeneous prizes to maximize expected total effort. The approach covers two information regimes and identifies a common principle: iron locally misordered incentive returns and assign prizes assortatively across the resulting grades. Under rank-only grading, assignments depend only on ordinal ranks. Ironing cumulative rank coefficients---via the least concave majorant or the pool-adjacent-violators algorithm---determines which adjacent ranks are pooled and which prizes are randomized within each grade. Under performance-contingent grading, assignments may depend on numerical effort. The optimum irons virtual ability, forms endogenous type grades, and assigns prize blocks assortatively across grades. A failing grade below a minimum passing effort and a collection of effort brackets implement the direct optimum while preserving full prize assignment.

Problem

• optimal grading
• all-pay contest
• heterogeneous prizes
• maximize expected total effort
• incentive returns

Innovation

• Optimal Grading
• All-Pay Contest
• Incentive Returns
• Assortative Assignment
• Least Concave Majorant