Revealed Preference Analysis of Shapley-Scarf Housing Markets

Umutcan Salman, Michele Lombardi, Francesco Ciardiello and Riccardo Saulle

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Abstract: We ask what the reallocation of indivisible objects reveals about the market that produced it. A central authority assigns the objects, after which recipients exchange them among themselves. Preferences are never observed, and individuals of the same type have identical preferences. A reallocation is rationalizable as Pareto efficient and individually rational exactly when a directed graph built from the data is acyclic, and as weak core-stable exactly when a mixed graph admits an orientation acyclic within types and free of alternating cycles. Deciding the latter is NP-complete, and on the single-crossing domain, although the test becomes more restrictive, it turns out to be more useful in practice. Both properties are less demanding than the strict core, so their rejection eliminates a broader set of possibilities. We apply the tests to administrative data on social housing lettings in England.

Date: 2025-12, Revised 2026-08
New Economics Papers: this item is included in nep-dcm and nep-mic
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