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Hedonic price equilibria, stable matching, and optimal transport: Equivalence, topology, and uniqueness. (English) Zbl 1183.91056
Summary: 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.

##### MSC:
 91B24 Microeconomic theory (price theory and economic markets) 91B68 Matching models 90B06 Transportation, logistics and supply chain management 90C05 Linear programming
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