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Revealed Preferences of One-Sided Matching

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  • Andrew Tai

Abstract

Consider the object allocation (one-sided matching) model of Shapley and Scarf (1974). When final allocations are observed but agents' preferences are unknown, when might the allocation be in the core? This is a one-sided analogue of the model in Echenique, Lee, Shum, and Yenmez (2013). I build a model in which the strict core is testable -- an allocation is "rationalizable" if there is a preference profile putting it in the core. In this manner, I develop a theory of the revealed preferences of one-sided matching. I study rationalizability in both non-transferrable and transferrable utility settings. In the non-transferrable utility setting, an allocation is rationalizable if and only if: whenever agents with the same preferences are in the same potential trading cycle, they receive the same allocation. In the transferrable utility setting, an allocation is rationalizable if and only if: there exists a price vector supporting the allocation as a competitive equilibrium; or equivalently, it satisfies a cyclic monotonicity condition. The proofs leverage simple graph theory and combinatorial optimization and tie together classic theories of consumer demand revealed preferences and competitive equilibrium.

Suggested Citation

  • Andrew Tai, 2022. "Revealed Preferences of One-Sided Matching," Papers 2210.14388, arXiv.org, revised Aug 2023.
    • Handle: RePEc:arx:papers:2210.14388
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    References listed on IDEAS

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    1. Alcalde-Unzu, Jorge & Molis, Elena, 2011. "Exchange of indivisible goods and indifferences: The Top Trading Absorbing Sets mechanisms," Games and Economic Behavior, Elsevier, vol. 73(1), pages 1-16, September.
    2. Roth, Alvin E & Xing, Xiaolin, 1997. "Turnaround Time and Bottlenecks in Market Clearing: Decentralized Matching in the Market for Clinical Psychologists," Journal of Political Economy, University of Chicago Press, vol. 105(2), pages 284-329, April.
    3. Alfred Galichon & Scott Duke Kominers & Simon Weber, 2019. "Costly Concessions: An Empirical Framework for Matching with Imperfectly Transferable Utility," Journal of Political Economy, University of Chicago Press, vol. 127(6), pages 2875-2925.
    4. Federico Echenique, 2008. "What Matchings Can Be Stable? The Testable Implications of Matching Theory," Mathematics of Operations Research, INFORMS, vol. 33(3), pages 757-768, August.
    5. Gerard Debreu, 1963. "On a Theorem of Scarf," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 30(3), pages 177-180.
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