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

  • Ivar Ekeland
  • Alfred Galichon

    ()

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

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File URL: http://hdl.handle.net/10.1007/s00199-012-0719-x
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Article provided by Springer & Society for the Advancement of Economic Theory (SAET) in its journal Economic Theory.

Volume (Year): 54 (2013)
Issue (Month): 3 (November)
Pages: 425-441

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Handle: RePEc:spr:joecth:v:54:y:2013:i:3:p:425-441
DOI: 10.1007/s00199-012-0719-x
Contact details of provider: Web page: http://www.springer.com

Web page: http://saet.uiowa.edu/

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  1. Laurens Cherchye & Bram De Rock & Frederic Vermeulen, 2010. "An Afriat theorem for the collective model of household consumption," ULB Institutional Repository 2013/131711, ULB -- Universite Libre de Bruxelles.
  2. M.J. Todd & A. Fostel & H.E. Scarf, 2004. "Two New Proofs of Afriat's Theorem," Econometric Society 2004 North American Summer Meetings 632, Econometric Society.
  3. Alvin E. Roth & Tayfun Sonmez & M. Utku Unver, 2003. "Kidney Exchange," Game Theory and Information 0308002, EconWPA.
  4. repec:dau:papers:123456789/4099 is not listed on IDEAS
  5. Cherchye, L.J.H. & de Rock, B. & Vermeulen, F.M.P., 2004. "The Collective Model of Household Consumption : A Nonparametric Characterization," Discussion Paper 2004-76, Tilburg University, Center for Economic Research.
  6. 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.
  7. 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, 01.
  8. Shapley, Lloyd & Scarf, Herbert, 1974. "On cores and indivisibility," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 23-37, March.
  9. John Quah, 2012. "A revealed preference test for weakly separable preferences," Economics Series Working Papers 601, University of Oxford, Department of Economics.
  10. 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.
  11. Alfred Galichon & Bernard Salanié, 2010. "Matching with Trade-offs: Revealed Preferences over Competiting Characteristics," Working Papers hal-00473173, HAL.
  12. Neil E. Gretsky & Joseph M. Ostroy & William R. Zame, 1990. "The Nonatomic Assignment Model," UCLA Economics Working Papers 605, UCLA Department of Economics.
  13. Forges, Françoise & Minelli, Enrico, 2009. "Afriat's theorem for general budget sets," Journal of Economic Theory, Elsevier, vol. 144(1), pages 135-145, January.
  14. Matzkin, Rosa L, 1991. "Axioms of Revealed Preference for Nonlinear Choice Sets," Econometrica, Econometric Society, vol. 59(6), pages 1779-86, November.
  15. W. E. Diewert, 1973. "Afriat and Revealed Preference Theory," Review of Economic Studies, Oxford University Press, vol. 40(3), pages 419-425.
  16. Varian, Hal R, 1982. "The Nonparametric Approach to Demand Analysis," Econometrica, Econometric Society, vol. 50(4), pages 945-73, July.
  17. 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.
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