A Note on the Strategic Vulnerability of the Boston Mechanism in Random Markets

TL;DR

This paper analyzes the Boston Mechanism's vulnerability in large random markets, showing that truthful reporting yields high preferences but equilibria lead to significantly worse outcomes as market size increases.

Contribution

It provides the first asymptotic analysis of the Boston Mechanism under equilibrium play, revealing its increasing vulnerability in large markets.

Findings

63% of students get their first choice under truthful reporting

The first-choice rate drops to zero in Nash equilibria as market size grows

Average student rank worsens dramatically in equilibrium, from 7th to 145th in 1,000-student markets

Abstract

We provide the first asymptotic analysis of the Boston Mechanism under equilibrium play in random markets. We provide two results. First, while 63\% of students receive their first preference under truthful reporting-outperforming any other known mechanism in the literature-this rate converges to zero in any Nash equilibrium of the corresponding preference revelation game as the market size grows. Second, we show there exists a Nash equilibrium where the average student receives a dramatically inferior assignment: in markets with 1,000 students, the average placement shifts from the 7th choice (under truthfulness) to the 145th choice, representing a change from logarithmic to nearly linear average rank.