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… 

Afriat ’ s theorem for indivisible goods ∗

We identify a natural counterpart of the standard GARP for demand data in which goods are all indivisible. We show that the new axiom (DARP, for ”discrete axiom of revealed preference”) is necessary

Afriat's Theorem for Indivisible Goods

Positively-homogeneous Konus-Divisia indices and their applications to demand analysis and forecasting

This paper is devoted to revealed preference theory and its applications to testing economic data for consistency with utility maximization hypothesis, construction of index numbers, and forecasting.

Revealed smooth nontransitive preferences

In the present paper, we are concerned with the behavioural consequences of consumers having nontransitive preference relations. Data sets consist of finitely many observations of price vectors and

Revealed smooth nontransitive preferences

In the present paper, we are concerned with the behavioural consequences of consumers having nontransitive preference relations. Data sets consist of finitely many observations of price vectors and

Inverse problems of demand analysis and their applications to computation of positively-homogeneous Konüs–Divisia indices and forecasting

Abstract According to Pareto’s theory of consumer demand a rational representative consumer should choose their consumption bundle as the solution of a mathematical programming problem of

Revealed Preference in a Discrete Consumption Space

We show that an agent maximizing some utility function on a discrete (as opposed to continuous) consumption space will obey the generalized axiom of revealed preference (GARP) so long as the agent

Essential data, budget sets and rationalization

According to a minimalist version of Afriat’s theorem, a consumer behaves as a utility maximizer if and only if a feasibility matrix associated with his choices is cyclically consistent. An

Inverse problems in Pareto’s demand theory and their applications to analysis of stock market crises

Abstract We develop an approach to the analysis of stock market crises based on the generalized nonparametric method. The generalized nonparametric method is based on solvability and regularization

References

SHOWING 1-10 OF 31 REFERENCES

Afriat's Theorem for General Budget Sets

An Afriat Theorem for the Collective Model of Household Consumption

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.

On cores and indivisibility

Revealed Preference and the Utility Function

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

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

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

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

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

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

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