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On the Revealed Preference Analysis of Stable Aggregate Matchings

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  • Thomas Demuynck
  • Umutcan Salman

Abstract

We extend the analysis of (Echenique, Lee, Shum, and Yenmez, 2013) by looking at the testable revealed preference restrictions for stable aggregate matchings with non-transferable utility. We rephrase their revealed preference test in terms of a bipartite graph. From this, we obtain an simple condition that verifies whether a given matching is rationalisable. Next, for a matching that is not rationalisable, we show how to find the minimal number of matches that needs to be removed in order to restore rationalisability. This produces a goodness-of-fit measure that indicates how close a matching is to being rationalisable. We also show that the related problem of finding the minimal number of types that we need to remove in order to obtain rationalisability is NP-hard. We provide two illustrations to demonstrate the usefulness of our results.

Suggested Citation

  • Thomas Demuynck & Umutcan Salman, 2020. "On the Revealed Preference Analysis of Stable Aggregate Matchings," Working Papers ECARES 2020-42, ULB -- Universite Libre de Bruxelles.
  • Handle: RePEc:eca:wpaper:2013/312868
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    References listed on IDEAS

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    3. Laurens Cherchye & Thomas Demuynck & Bram De Rock & Frederic Vermeulen, 2017. "Household Consumption When the Marriage Is Stable," American Economic Review, American Economic Association, vol. 107(6), pages 1507-1534, June.
    4. Federico Echenique & Sangmok Lee & Matthew Shum, 2011. "The Money Pump as a Measure of Revealed Preference Violations," Journal of Political Economy, University of Chicago Press, vol. 119(6), pages 1201-1223.
    5. Alan Agresti & Dennis Wackerly & James Boyett, 1979. "Exact conditional tests for cross-classifications: Approximation of attained significance levels," Psychometrika, Springer;The Psychometric Society, vol. 44(1), pages 75-83, March.
    6. Federico Echenique & Sangmok Lee & Matthew Shum & M. Bumin Yenmez, 2013. "The Revealed Preference Theory of Stable and Extremal Stable Matchings," Econometrica, Econometric Society, vol. 81(1), pages 153-171, January.
    7. 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.
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    Cited by:

    1. Federico Echenique & SangMok Lee & Matthew Shum & M. Bumin Yenmez, 2021. "Stability and Median Rationalizability for Aggregate Matchings," Games, MDPI, Open Access Journal, vol. 12(2), pages 1-15, April.

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    More about this item

    Keywords

    Revealed preference theory; com- putational complexity; stability; two-sided matching markets;
    All these keywords.

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory

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