Quota Mechanisms: Finite-Sample Optimality and Robustness

TL;DR

This paper studies the finite-sample performance and robustness of quota mechanisms, providing optimality guarantees and analyzing their sensitivity to distributional errors and agents' beliefs.

Contribution

It introduces a new optimal transport approach to derive ex-post error guarantees and assesses the robustness of quotas to distributional and belief errors.

Findings

Quota mechanisms have a provable ex-post error guarantee.

They are robust to agents' beliefs about each other.

Performance is sensitive to errors in the estimated type distribution.

Abstract

A quota mechanism, such as a mandatory grading curve, links together multiple decisions. We analyze the performance of quota mechanisms when the number of linked decisions is finite and the designer has imperfect knowledge of the type distribution. Using a new optimal transport approach, we derive an ex-post decision error guarantee for quota mechanisms. This guarantee cannot be improved by any mechanisms without transfers. We quantify the sensitivity of quota mechanisms to errors in the designer's estimate of the type distribution. Finally, we show that quotas are robust to a range of agents' beliefs about each other.