Efficiency Adjustments Break the Logarithmic Rank Barrier

2026-08-05

AI Summary

This study addresses the limitations of the traditional Deferred Acceptance (DA) mechanism, which achieves only logarithmic expected average rank in i.i.d. matching markets. Focusing on the Efficiency-adjusted Deferred Acceptance (EADA) mechanism, the paper establishes the first asymptotic upper bound on the expected average rank for EADA and a broader class of Pareto-efficient improvement mechanisms. By integrating probabilistic analysis with mechanism design theory and leveraging Pareto efficiency along with weak Pareto dominance conditions, the authors prove that EADA attains an expected average rank of at most \(4 \log \log n + O(1)\), substantially surpassing DA’s logarithmic barrier. These results extend to many-to-one matching settings and random markets with correlated preferences.

Abstract

We study the expected average rank achieved by the Efficiency-Adjusted Deferred Acceptance (EADA) mechanism in i.i.d.\ matching markets. While student-proposing Deferred Acceptance gives students an expected average rank of logarithmic order, we prove that EADA's expected average rank is at most $4\log\log n+O(1)$. Therefore, EADA improves the asymptotic order of students' assignments. At the cost of a weaker bound, $O((\log\log n)^2)$, we extend this conclusion to a much larger class of mechanisms. Namely, every Pareto-efficient mechanism that weakly Pareto-dominates DA breaks DA's logarithmic barrier. These are the first asymptotic guarantees for the expected average rank of EADA and of the broader class of Pareto-efficient improvements of DA. The conclusions extend to many-to-one markets with bounded quotas and random markets with correlated preferences.

Problem

• matching markets
• Deferred Acceptance
• average rank
• Pareto efficiency
• asymptotic performance

Innovation

• Efficiency-Adjusted Deferred Acceptance
• average rank
• logarithmic barrier
• Pareto efficiency
• matching markets