Payoff equivalence of efficient mechanisms in large matching markets

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 provide a broad set of circumstances under which, as the market grows large, all Pareto efficient mechanisms - including top trading cycles (with an arbitrary ownership structure), serial dictatorship (with an arbitrary serial order), and their randomized variants - produce a distribution of agent utilities that in the limit coincides with the utilitarian upper bound. This implies that Pareto efficient mechanisms are uniformly asymptotically payoff equivalent "up to the renaming of agents." Hence, 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.