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On the revealed preference analysis of stable aggregate matchings

Author

Listed:
  • Demuynck, Thomas

    (Ecares, Université Libre de Bruxelles)

  • Salman, Umutcan

    (Ecares, Université Libre de Bruxelles)

Abstract

Echenique, Lee, Shum, and Yenmez (2013) established the testable revealed preference restrictions for stable aggregate matching with transferable (TU) and non-transferable utility (NTU) and for extremal stable matchings. In this paper, we rephrase their restrictions in terms of properties on a corresponding bipartite graph. From this, we obtain a simple condition that verifies whether a given aggregate matching is rationalisable. For matchings that are not rationalisable, we provide a simple greedy algorithm that computes the minimum number of matches that needs to be removed to obtain a rationalisable matching. We also show that the related problem of finding the minimum number of types that we need to remove in order to obtain a rationalisable matching is NP-complete.

Suggested Citation

  • Demuynck, Thomas & Salman, Umutcan, 2022. "On the revealed preference analysis of stable aggregate matchings," Theoretical Economics, Econometric Society, vol. 17(4), November.
    • Handle: RePEc:the:publsh:4723
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    References listed on IDEAS

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    1. Arnaud Dupuy & Alfred Galichon, 2014. "Personality Traits and the Marriage Market," Journal of Political Economy, University of Chicago Press, vol. 122(6), pages 1271-1319.
    2. 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.
    3. 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.
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    6. 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.
    7. Jose Apesteguia & Miguel A. Ballester, 2015. "A Measure of Rationality and Welfare," Journal of Political Economy, University of Chicago Press, vol. 123(6), pages 1278-1310.
    8. Mark Dean & Daniel Martin, 2016. "Measuring Rationality with the Minimum Cost of Revealed Preference Violations," The Review of Economics and Statistics, MIT Press, vol. 98(3), pages 524-534, July.
    9. Demuynck, Thomas & Salman, Umutcan, 2022. "On the revealed preference analysis of stable aggregate matchings," Theoretical Economics, Econometric Society, vol. 17(4), November.
    10. Varian, Hal R., 1990. "Goodness-of-fit in optimizing models," Journal of Econometrics, Elsevier, vol. 46(1-2), pages 125-140.
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    12. Hu, Gaoji & Li, Jiangtao & Tang, Rui, 2020. "The revealed preference theory of stable matchings with one-sided preferences," Games and Economic Behavior, Elsevier, vol. 124(C), pages 305-318.
    13. Arnaud Dupuy & Alfred Galichon, 2014. "Personality traits and the marriage market," SciencePo Working papers hal-03470458, HAL.
    14. 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.
    15. Arnaud Dupuy & Alfred Galichon, 2014. "Personality traits and the marriage market," Post-Print hal-03470458, HAL.
    16. Laurens Cherchye & Thomas Demuynck & Bram De Rock & Joshua Lanier, 2020. "Are Consumers Rational ?Shifting the Burden of Proof," Working Papers ECARES 2020-19, ULB -- Universite Libre de Bruxelles.
    17. Arnaud Dupuy & Alfred Galichon, 2014. "Personality traits and the marriage market," SciencePo Working papers Main hal-03470458, HAL.
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    19. Varian, Hal R., 1985. "Non-parametric analysis of optimizing behavior with measurement error," Journal of Econometrics, Elsevier, vol. 30(1-2), pages 445-458.
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    1. Demuynck, Thomas & Salman, Umutcan, 2022. "On the revealed preference analysis of stable aggregate matchings," Theoretical Economics, Econometric Society, vol. 17(4), November.
    2. Federico Echenique & SangMok Lee & Matthew Shum & M. Bumin Yenmez, 2021. "Stability and Median Rationalizability for Aggregate Matchings," Games, MDPI, vol. 12(2), pages 1-15, April.

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    More about this item

    Keywords

    Revealed preference theory; two-sided matching markets; stability; computational complexity; matroid;
    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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