Top Trading Cycles in Prioritized Matching: An Irrelevance of Priorities in Large Markets

We study top trading cycles in a two-sided matching environment (Abdulkadiroglu and Sonmez (2003)) under the assumption that individuals’ preferences and objects’ priorities are drawn iid uniformly. We show that the number of individuals/objects assigned at each round follows a simple Markov chain and we explicitly derive the transition probabilities. This Markov property is used to shed light on the role priorities play in TTC. We show that, as the market grows large, the effect of priorities in TTC disappears, leading in the limit to an assignment that entails virtually the same amount of justified envy as does RSD. JEL Classification Numbers: C70, D47, D61, D63.