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

20 Pages Posted: 5 Dec 2010 Last revised: 30 Jan 2012

Ivar Ekeland

University of British Columbia (UBC) - Faculty of Education; Université Paris Dauphine - CEREMADE

Alfred Galichon

NYU, Department of Economics and Courant Institute

Date Written: January 30, 2012

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.

Keywords: Revealed Preferences, Afriat’s Theorem, Optimal Assignments, Indivisible Allocations

JEL Classification: D11, C60, C78

Suggested Citation

Ekeland, Ivar and Galichon, Alfred, The Housing Problem and Revealed Preference Theory: Duality and an Application (January 30, 2012). Available at SSRN: https://ssrn.com/abstract=1719864 or http://dx.doi.org/10.2139/ssrn.1719864

Ivar Ekeland

University of British Columbia (UBC) - Faculty of Education ( email )

Université Paris Dauphine - CEREMADE ( email )

Place du Marechal de Lattre de Tassigny
Paris Cedex 16, 75775
France

Alfred Galichon (Contact Author)

NYU, Department of Economics and Courant Institute ( email )

269 Mercer Street, 7th Floor
New York, NY 10011
United States

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