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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
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  1. Laurens Cherchye & Bram De Rock & Frederic Vermeulen, 2007. "The Collective Model of Household Consumption: A nonparametric characterization," ULB Institutional Repository 2013/98559, ULB -- Universite Libre de Bruxelles.
  2. Herbert E. Scarf & Ana Fostel & Michael J. Todd, 2004. "Two New Proofs of Afriat's Theorem," Yale School of Management Working Papers ysm377, Yale School of Management.
  3. 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.
  4. Roth, Alvin & Ünver, M. Utku & Sönmez, Tayfun, 2004. "Kidney Exchange," Scholarly Articles 2580565, Harvard University Department of Economics.
  5. Ivar Ekeland & Alfred Galichon & Marc Henry, 2010. "Optimal transportation and the falsifiability of incompletely specified economic models," Economic Theory, Society for the Advancement of Economic Theory (SAET), vol. 42(2), pages 355-374, February.
  6. Varian, Hal R, 1982. "The Nonparametric Approach to Demand Analysis," Econometrica, Econometric Society, vol. 50(4), pages 945-73, July.
  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. Ivar Ekeland, 2010. "Notes on optimal transportation," Economic Theory, Society for the Advancement of Economic Theory (SAET), vol. 42(2), pages 437-459, February.
  9. Alfred Galichon & Bernard Salanié, 2010. "Matching with Trade-Offs: Revealed Preferences over Competing Characteristics," Sciences Po publications info:hdl:2441/1293p84sf58, Sciences Po.
  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. Shapley, Lloyd & Scarf, Herbert, 1974. "On cores and indivisibility," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 23-37, March.
  12. Francoise Forges & Enrico Minelli, 2006. "Afriat's Theorem for General Budget Sets," Working Papers ubs0609, University of Brescia, Department of Economics.
  13. Neil E. Gretsky & Joseph M. Ostroy & William R. Zame, 1990. "The Nonatomic Assignment Model," UCLA Economics Working Papers 605, UCLA Department of Economics.
  14. Matzkin, Rosa L, 1991. "Axioms of Revealed Preference for Nonlinear Choice Sets," Econometrica, Econometric Society, vol. 59(6), pages 1779-86, November.
  15. repec:dau:papers:123456789/4099 is not listed on IDEAS
  16. W. E. Diewert, 1973. "Afriat and Revealed Preference Theory," Review of Economic Studies, Oxford University Press, vol. 40(3), pages 419-425.
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