Interpolating between matching and hedonic pricing models

Research Article
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Abstract

We consider the theoretical properties of a model which encompasses bipartite matching under transferable utility on the one hand and hedonic pricing on the other. This framework is intimately connected to tripartite matching problems (known as multi-marginal optimal transport problems in the mathematical literature). We exploit this relationship in two main ways; first, we show that a known structural result from multi-marginal optimal transport can be used to establish an upper bound on the dimension of the support of stable matchings. Next, assuming the distribution of agents on one side of the market is continuous, we identify a condition on their preferences that ensures purity and uniqueness of the stable matching; this condition is a variant of a known condition in the mathematical literature, which guarantees analogous properties in the multi-marginal optimal transport problem. We exhibit several examples of surplus functions for which our condition is satisfied, as well as some for which it fails.

Keywords

Matching under transferable utility Hedonic pricing Optimal transport Multi-marginal problems Purity Uniqueness 

JEL Classification

C78 

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematical and Statistical Sciences, 632 CABUniversity of AlbertaEdmontonCanada

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