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The Housing Problem and Revealed Preference Theory: Duality and an application

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  • Ivar Ekeland

    (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique)

  • Alfred Galichon

    (ECON - Département d'économie (Sciences Po) - Sciences Po - Sciences Po - CNRS - Centre National de la Recherche Scientifique)

Abstract

This paper exhibits a duality between the theory of revealed preference of Afriat and the housing allocation problem of Shapley and Scarf. In particular, it is shown that Afriat's theorem can be interpreted as a second welfare theorem in the housing problem. Using this duality, the revealed preference problem is connected to an optimal assignment problem, and a geometrical characterization of the rationalizability of experiment data is given. This allows in turn to give new indices of rationalizability of the data and to define weaker notions of rationalizability, in the spirit of Afriat's efficiency index.

Suggested Citation

  • Ivar Ekeland & Alfred Galichon, 2013. "The Housing Problem and Revealed Preference Theory: Duality and an application," Post-Print hal-01059558, HAL.
    • Handle: RePEc:hal:journl:hal-01059558
    DOI: 10.1007/s00199-012-0719-x
    Note: View the original document on HAL open archive server: https://sciencespo.hal.science/hal-01059558v1
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    References listed on IDEAS

    as
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    Cited by:

    1. Echenique, Federico & Galichon, Alfred, 2017. "Ordinal and cardinal solution concepts for two-sided matching," Games and Economic Behavior, Elsevier, vol. 101(C), pages 63-77.
    2. Nikolay Klemashev & Alexander Shananin, 2015. "Positively-homogeneous Konus-Divisia indices and their applications to demand analysis and forecasting," Papers 1501.05771, arXiv.org.
    3. Alfred Galichon & John Quah, 2013. "Symposium on revealed preference analysis," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 54(3), pages 419-423, November.
    4. Agatsuma, Yasushi, 2016. "Testable implications of the core in TU market games," Journal of Mathematical Economics, Elsevier, vol. 64(C), pages 23-29.
    5. Forges, Françoise & Iehlé, Vincent, 2014. "Afriat’s theorem for indivisible goods," Journal of Mathematical Economics, Elsevier, vol. 54(C), pages 1-6.
    6. Hans Keiding & Mich Tvede, 2013. "Revealed smooth nontransitive preferences," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 54(3), pages 463-484, November.
    7. repec:hal:spmain:info:hdl:2441/t2p3rkl1d8gqrqvgeigklj2qg is not listed on IDEAS
    8. Echenique, Federico & Galichon, Alfred, 2017. "Ordinal and cardinal solution concepts for two-sided matching," Games and Economic Behavior, Elsevier, vol. 101(C), pages 63-77.

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    More about this item

    Keywords

    Afriat's theorem; Indivisible allocations; Optimal assignment; Revealed preferences;
    All these keywords.

    JEL classification:

    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

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