Asymptotic Equivalence of Immediate and Deferred Acceptance

2026/07/27 by Josue Ortega
#econ.TH

paper · pdf

Abstract

Immediate Acceptance (IA, also known as the Boston mechanism) is commonly used to assign students to schools because it produces a Pareto-efficient matching if parents report their preferences over schools truthfully, unlike student-proposing Deferred Acceptance (DA). In this paper, we ask: does IA produce meaningfully better average ranks than DA, conditional on truth-telling? We show that, in i.i.d. one-to-one random markets, IA's expected average rank is asymptotically log n, just like DA's. Therefore, IA's Pareto efficiency does not translate into a first-order improvement in expected average rank. This conclusion extends to variations of IA as well as to many-to-one markets.

Citations

• Asymptotic Equilibrium Analysis of the Boston Mechanism
• The Large and Likely Inefficiency of Stable Matching Mechanisms
• Asymptotic welfare performance of Boston assignment algorithms
• Partial Strategyproofness: Relaxing Strategyproofness for the Random Assignment Problem
• College Admissions and the Stability of Marriage

Related

• What Pareto-Efficiency Adjustments Cannot Fix
• Playing on a Level Field: Sincere and Sophisticated Players in the\n Boston Mechanism with a Coarse Priority Structure
• Trade-offs in School Choice: Comparing Deferred Acceptance, the Naive and the Classic Boston Mechanism
• The Large and Likely Inefficiency of Stable Matching Mechanisms
• On the Susceptibility of the Deferred Acceptance Algorithm