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Hedonic price equilibria, stable matching, and optimal transport: equivalence, topology, and uniqueness

Authors: Pierre-André Chiappori , Robert McCann and Lars Nesheim
Date: 28 September 2007
Type: cemmap Working Paper, CWP23/07
DOI: 10.1920/wp.cem.2007.2307

Abstract

Hedonic pricing with quasilinear preferences is shown to be equivalent to stable matching with transferable utilities and a participation constraint, and to an optimal transportation (Monge-Kantorovich) linear programming problem. Optimal assignments in the latter correspond to stable matchings, and to hedonic equilibria. These assignments are shown to exist in great generality; their marginal indirect payoffs with respect to agent type are shown to be unique whenever direct payoffs vary smoothly with type. Under a generalized Spence-Mirrlees condition the assignments are shown to be unique and to be pure, meaning the matching is one-to-one outside a negligible set. For smooth problems set on compact, connected type spaces such as the circle, there is a topological obstruction to purity, but we give a weaker condition still guaranteeing uniqueness of the stable match. An appendix resolves an old problem (# 111) of Birkhoff in probability and statistics [5], by giving a necessary and sufficient condition on the support of a joint probability to guarantee extremality among all joint measures with the same marginals.

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Now published:
Pierre-André Chiappori, Robert McCann and Lars Nesheim February 2010, Hedonic price equilibria, stable matching, and optimal transport: equivalence, topology, and uniqueness, Journal Article

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