Chiappori, PA; McCann, RJ; Nesheim, LP; (2010) Hedonic price equilibria, stable matching, and optimal transport: equivalence, topology, and uniqueness. ECON THEOR , 42 (2) 317 - 354. 10.1007/s00199-009-0455-z.

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Abstract

Hedonic pricing with quasi-linear 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 (also known as a twist 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.

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