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

Pierre Chiappori, Robert McCann and Lars Nesheim
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Robert McCann: Institute for Fiscal Studies and University of Toronto

No CWP23/07, CeMMAP working papers from Centre for Microdata Methods and Practice, Institute for Fiscal Studies

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.

Date: 2007-09-28
New Economics Papers: this item is included in nep-gth
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Journal Article: Hedonic price equilibria, stable matching, and optimal transport: equivalence, topology, and uniqueness (2010)
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