We study Pareto eﬀicient mechanisms in matching markets when the number of agents is large and individual preferences are randomly drawn from a class of distributions, allowing for both common and idiosyncratic shocks. We show that, as the market grows large, all Pareto eﬀicient mechanisms — including top trading cycles, serial dictatorship, and their randomized variants — are uniformly asymptotically payoﬀ equivalent “up to the renaming of agents,” yielding the utilitarian upper bound in the limit. This result implies that, when the conditions of our model are met, policy makers need not discriminate among Pareto eﬀicient mechanisms based on the aggregate payoﬀ distribution of participants.
Che, Yeon-Koo and Tercieux, Olivier, "Payoff Equivalence of Efficient Mechanisms in Large Matching Markets" (2015). Cowles Foundation Discussion Papers. 2452.