IDEAS home Printed from https://ideas.repec.org/a/spr/joecth/v54y2013i3p425-441.html
   My bibliography  Save this article

The housing problem and revealed preference theory: duality and an application

Author

Listed:
  • Ivar Ekeland
  • Alfred Galichon

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. Copyright Springer-Verlag 2013

Suggested Citation

  • Ivar Ekeland & Alfred Galichon, 2013. "The housing problem and revealed preference theory: duality and an application," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 54(3), pages 425-441, November.
    • Handle: RePEc:spr:joecth:v:54:y:2013:i:3:p:425-441
    DOI: 10.1007/s00199-012-0719-x
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00199-012-0719-x
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00199-012-0719-x?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Laurens Cherchye & Bram De Rock & Frederic Vermeulen, 2007. "The Collective Model of Household Consumption: A Nonparametric Characterization," Econometrica, Econometric Society, vol. 75(2), pages 553-574, March.
    2. Varian, Hal R, 1982. "The Nonparametric Approach to Demand Analysis," Econometrica, Econometric Society, vol. 50(4), pages 945-973, July.
    3. A. Fostel & H. Scarf & M. Todd, 2004. "Two new proofs of Afriat’s theorem," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 24(1), pages 211-219, July.
    4. Forges, Françoise & Minelli, Enrico, 2009. "Afriat's theorem for general budget sets," Journal of Economic Theory, Elsevier, vol. 144(1), pages 135-145, January.
    5. Alvin E. Roth & Tayfun Sönmez & M. Utku Ünver, 2004. "Kidney Exchange," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 119(2), pages 457-488.
    6. Szenberg, Michael & Ramrattan, Lall & Gottesman, Aron A. (ed.), 2006. "Samuelsonian Economics and the Twenty-First Century," OUP Catalogue, Oxford University Press, number 9780199298839.
    7. Gretsky, Neil E & Ostroy, Joseph M & Zame, William R, 1992. "The Nonatomic Assignment Model," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 2(1), pages 103-127, January.
    8. Cherchye, Laurens & De Rock, Bram & Vermeulen, Frederic, 2010. "An Afriat Theorem for the collective model of household consumption," Journal of Economic Theory, Elsevier, vol. 145(3), pages 1142-1163, May.
    9. 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.
    10. 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.
    11. Ivar Ekeland & Alfred Galichon & Marc Henry, 2010. "Optimal transportation and the falsifiability of incompletely specified economic models," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 42(2), pages 355-374, February.
    12. Shapley, Lloyd & Scarf, Herbert, 1974. "On cores and indivisibility," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 23-37, March.
    13. repec:hal:spmain:info:hdl:2441/1293p84sf58s482v2dpn0gsd67 is not listed on IDEAS
    14. Salanié, Bernard & Galichon, Alfred, 2010. "Matching with Trade-offs: Revealed Preferences over Competing Characteristics," CEPR Discussion Papers 7858, C.E.P.R. Discussion Papers.
    15. 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.
    16. Matzkin, Rosa L, 1991. "Axioms of Revealed Preference for Nonlinear Choice Sets," Econometrica, Econometric Society, vol. 59(6), pages 1779-1786, November.
    17. John Quah, 2012. "A revealed preference test for weakly separable preferences," Economics Series Working Papers 601, University of Oxford, Department of Economics.
    18. 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.
    19. repec:dau:papers:123456789/4099 is not listed on IDEAS
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. Forges, Françoise & Iehlé, Vincent, 2014. "Afriat’s theorem for indivisible goods," Journal of Mathematical Economics, Elsevier, vol. 54(C), pages 1-6.
    3. 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.
    4. 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.
    5. 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.
    6. Nikolay Klemashev & Alexander Shananin, 2015. "Positively-homogeneous Konus-Divisia indices and their applications to demand analysis and forecasting," Papers 1501.05771, arXiv.org.
    7. Agatsuma, Yasushi, 2016. "Testable implications of the core in TU market games," Journal of Mathematical Economics, Elsevier, vol. 64(C), pages 23-29.
    8. repec:hal:spmain:info:hdl:2441/t2p3rkl1d8gqrqvgeigklj2qg is not listed on IDEAS

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. repec:spo:wpecon:info:hdl:2441/5rkqqmvrn4tl22s9mc0o6ctj2 is not listed on IDEAS
    2. Ian Crawford & Bram De Rock, 2014. "Empirical Revealed Preference," Annual Review of Economics, Annual Reviews, vol. 6(1), pages 503-524, August.
    3. Dziewulski, Paweł & Lanier, Joshua & Quah, John K.-H., 2024. "Revealed preference and revealed preference cycles: A survey," Journal of Mathematical Economics, Elsevier, vol. 113(C).
    4. repec:hal:wpspec:info:hdl:2441/5rkqqmvrn4tl22s9mc0o6ctj2 is not listed on IDEAS
    5. Ivar Ekeland & Alfred Galichon, 2013. "The Housing Problem and Revealed Preference Theory: Duality and an application," SciencePo Working papers Main hal-01059558, HAL.
    6. repec:dau:papers:123456789/10574 is not listed on IDEAS
    7. Thomas Demuynck & John Rehbeck, 2023. "Computing revealed preference goodness-of-fit measures with integer programming," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 76(4), pages 1175-1195, November.
    8. 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.
    9. Pawe{l} Dziewulski & Joshua Lanier & John K. -H. Quah, 2024. "Revealed preference and revealed preference cycles: a survey," Papers 2405.08459, arXiv.org.
    10. repec:hal:spmain:info:hdl:2441/5rkqqmvrn4tl22s9mc0o6ctj2 is not listed on IDEAS
    11. Ivar Ekeland & Alfred Galichon, 2013. "The Housing Problem and Revealed Preference Theory: Duality and an application," SciencePo Working papers hal-01059558, HAL.
    12. repec:spo:wpmain:info:hdl:2441/5rkqqmvrn4tl22s9mc0o6ctj2 is not listed on IDEAS
    13. Kohei Shiozawa, 2015. "Revealed Preference Test and Shortest Path Problem; Graph Theoretic Structure of the Rationalizability Test," Discussion Papers in Economics and Business 15-17-Rev., Osaka University, Graduate School of Economics, revised Jul 2015.
    14. Smeulders, Bart & Crama, Yves & Spieksma, Frits C.R., 2019. "Revealed preference theory: An algorithmic outlook," European Journal of Operational Research, Elsevier, vol. 272(3), pages 803-815.
    15. Ivar Ekeland & Alfred Galichon, 2021. "The housing problem and revealed preference theory: duality and an application," Papers 2102.02593, arXiv.org.
    16. Demuynck, Thomas & Hjertstrand, Per, 2019. "Samuelson's Approach to Revealed Preference Theory: Some Recent Advances," Working Paper Series 1274, Research Institute of Industrial Economics.
    17. Fabrice Talla Nobibon & Laurens Cherchye & Yves Crama & Thomas Demuynck & Bram De Rock & Frits C. R. Spieksma, 2016. "Revealed Preference Tests of Collectively Rational Consumption Behavior: Formulations and Algorithms," Operations Research, INFORMS, vol. 64(6), pages 1197-1216, December.
    18. Alan Beggs, 2021. "Afriat and arbitrage," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 9(2), pages 167-176, October.
    19. Kohei Shiozawa, 2015. "Revealed Preference Test and Shortest Path Problem; Graph Theoretic Structure of the Rationalizability Test," Discussion Papers in Economics and Business 15-17-Rev.2, Osaka University, Graduate School of Economics, revised Aug 2016.
    20. Laurens Cherchye & Bram De Rock & Vincenzo Platino, 2013. "Private versus public consumption within groups: testing the nature of goods from aggregate data," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 54(3), pages 485-500, November.
    21. Polisson, Matthew & Renou, Ludovic, 2016. "Afriat’s Theorem and Samuelson’s ‘Eternal Darkness’," Journal of Mathematical Economics, Elsevier, vol. 65(C), pages 36-40.
    22. Françoise Forges & Vincent Iehlé, 2013. "Essential data, budget sets and rationalization," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 54(3), pages 449-461, November.
    23. Avner Seror, 2022. "The Priced Survey Methodology," AMSE Working Papers 2224, Aix-Marseille School of Economics, France.
    24. repec:hal:wpaper:halshs-00870052 is not listed on IDEAS
    25. John Quah & Hiroki Nishimura & Efe A. Ok, 2013. "A Unified Approach to Revealed Preference Theory: The Case of Rational Choice," Economics Series Working Papers 686, University of Oxford, Department of Economics.
    26. Forges, Françoise & Iehlé, Vincent, 2014. "Afriat’s theorem for indivisible goods," Journal of Mathematical Economics, Elsevier, vol. 54(C), pages 1-6.

    More about this item

    Keywords

    Revealed preferences; Afriat’s theorem; Optimal assignments; Indivisible allocations; Primary D11; Secondary C60; C78;
    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:joecth:v:54:y:2013:i:3:p:425-441. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.