Top Trading Cycles in Large Markets: The Asymptotic Irrelevance of Priorities

2026-07-12

AI Summary

This study investigates whether the Top Trading Cycles (TTC) mechanism can consistently achieve both efficiency and fairness in large markets, with particular attention to whether its reliance on priority structures diminishes as market size grows. Leveraging random matching theory, asymptotic analysis, and comparative mechanism design under standard assumptions of random preferences and priorities, the paper establishes—for the first time—that as market size tends to infinity, the influence of priorities in TTC asymptotically vanishes. Consequently, the allocation outcome of TTC becomes asymptotically equivalent to that of Random Serial Dictatorship—a mechanism that entirely disregards priorities—in terms of the incidence of justified envy. This result challenges the conventional view that TTC effectively balances fairness and efficiency in practical applications.

Abstract

Top Trading Cycles (TTC) is Pareto efficient and strategy-proof and explicitly uses agents' priorities. Although TTC favors higher-priority agents in each round, we show that this priority advantage vanishes as the market grows large under a canonical random model of preferences and priorities. In the limit, TTC produces assignments with virtually the same incidence of justified envy as Random Serial Dictatorship (RSD) -- a mechanism entirely blind to priorities. This stark asymptotic equivalence implies that TTC effectively fails to satisfy standard fairness criteria in large markets, casting significant doubt on its practical appeal for balancing efficiency and fairness.

Problem

• Top Trading Cycles
• large markets
• priorities
• fairness
• justified envy

Innovation

• Top Trading Cycles
• asymptotic equivalence
• justified envy
• priority
• large markets