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

Ivar Ekeland (1) , Alfred Galichon (2)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 ECON - Département d'économie (Sciences Po)

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: Afriat's theorem; Indivisible allocations; Optimal assignment; Revealed preferences

Domains: Economics and Finance

Ivar Ekeland, Alfred Galichon. The Housing Problem and Revealed Preference Theory: Duality and an application. Economic Theory, 2013, 54 (3), pp.425-441. ⟨10.1007/s00199-012-0719-x⟩. ⟨hal-01059558⟩