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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," SciencePo Working papers Main hal-01059558, HAL.
    • Handle: RePEc:hal:spmain:hal-01059558
    DOI: 10.1007/s00199-012-0719-x
    Note: View the original document on HAL open archive server: https://sciencespo.hal.science/hal-01059558
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    References listed on IDEAS

    as
    1. Forges, Françoise & Minelli, Enrico, 2009. "Afriat's theorem for general budget sets," Journal of Economic Theory, Elsevier, vol. 144(1), pages 135-145, January.
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    3. Alfred Galichon & Bernard Salanié, 2010. "Matching with Trade-offs: Revealed Preferences over Competiting Characteristics," Working Papers hal-00473173, HAL.
    4. repec:dau:papers:123456789/4099 is not listed on IDEAS
    5. Shapley, Lloyd & Scarf, Herbert, 1974. "On cores and indivisibility," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 23-37, March.
    6. Ivar Ekeland, 2010. "Notes on optimal transportation," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 42(2), pages 437-459, February.
    7. 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.
    8. Matzkin, Rosa L, 1991. "Axioms of Revealed Preference for Nonlinear Choice Sets," Econometrica, Econometric Society, vol. 59(6), pages 1779-1786, November.
    9. W. E. Diewert, 1973. "Afriat and Revealed Preference Theory," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 40(3), pages 419-425.
    Full references (including those not matched with items on IDEAS)

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