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

@article{Ekeland2012TheHP, title={The housing problem and revealed preference theory: duality and an application}, author={Ivar Ekeland and Alfred Galichon}, journal={Economic Theory}, year={2012}, volume={54}, pages={425-441} }

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…

## 19 Citations

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## References

SHOWING 1-10 OF 31 REFERENCES

### Afriat's Theorem for General Budget Sets

- Economics, MathematicsJ. Econ. Theory
- 2009

### An Afriat Theorem for the Collective Model of Household Consumption

- EconomicsJ. Econ. Theory
- 2010

This work provides a nonparametric 'revealed preference' characterization of rational household behavior in terms of the collective consumption model, while accounting for general individual preferences that can be non-convex, and implies the Collective Axiom of Revealed Preference (CARP) as a testable necessary and sufficient condition for data consistency with collective rationality.

### Revealed Preference and the Utility Function

- Economics
- 1950

Professor Samuelson's "revealed preference" approach' has proved to be a useful basis for deriving a considerable part of the static theory of consumer's choice. Its exisLing versions are not…

### A revealed preference test for weakly separable preferences

- Economics
- 2012

Consider a finite data set of price vectors and consumption bundles; under what conditions will there be a weakly separable utlity function that rationalizes the data? This paper shows that…

### The nonatomic assignment model

- Economics
- 1992

SummaryWe formulate a model with a continuum of individuals to be assigned to a continuum of different positions which is an extension of the finite housing market version due to Shapley and Shubik.…

### Matching with Trade-Offs: Revealed Preferences Over Competing Characteristics

- Economics
- 2009

It is shown how data on the covariation of the types of the partners in observed matches can be used to estimate the parameters that define social preferences over matches, both nonparametric and parametric procedures that are very easy to use in applications.

### The Collective Model of Household Consumption: A Nonparametric Characterization

- Economics
- 2004

We provide a nonparametric characterization of a general collective model for household consumption, which includes externalities and public consumption. Next, we establish testable necessary and…

### The Revealed Preference Theory of Stable and Extremal Stable Matchings

- Economics, Mathematics
- 2010

We investigate the testable implications of the theory of stable matchings. We provide a characterization of the matchings that are rationalizable as stable matchings when agents' preferences are…

### The assignment game I: The core

- Economics
- 1971

The assignment game is a model for a two-sided market in which a product that comes in large, indivisible units (e.g., houses, cars, etc.) is exchanged for money, and in which each participant either…