Efficiency and Stability in Large Matching Markets

We study efficient and stable mechanisms in matching markets when the number of agents is large and individuals’ preferences are drawn randomly from a class of distributions allowing for both common and idiosyncratic components. In this context, as the market grows large, all Pareto efficient mechanisms—including top trading cycles, serial dictatorship, and their randomized variants—are asymptotically payoff equivalent “up to the renaming of agents,” yielding the utilitarian upper bound in the limit. If agents’ priorities with objects are also randomly drawn but their common values for objects are heterogenous, then well-known mechanisms such as deferred acceptance and top trading cycle mechanisms fail either efficiency or stability even in the asymptotic sense. We propose a new mechanism that is asymptotically efficient, asymptotically stable and asymptotically incentive compatible.