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Interpolating between matching and hedonic pricing models

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  • Brendan Pass

    (University of Alberta)

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.

Suggested Citation

  • Brendan Pass, 2019. "Interpolating between matching and hedonic pricing models," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 67(2), pages 393-419, March.
    • Handle: RePEc:spr:joecth:v:67:y:2019:i:2:d:10.1007_s00199-018-1126-8
    DOI: 10.1007/s00199-018-1126-8
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    References listed on IDEAS

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    1. Pierre-André Chiappori & Robert McCann & Lars Nesheim, 2010. "Hedonic price equilibria, stable matching, and optimal transport: equivalence, topology, and uniqueness," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 42(2), pages 317-354, February.
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    9. Ivar Ekeland, 2010. "Existence, uniqueness and efficiency of equilibrium in hedonic markets with multidimensional types," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 42(2), pages 275-315, February.
    10. G. Carlier & I. Ekeland, 2010. "Matching for teams," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 42(2), pages 397-418, February.
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    Cited by:

    1. Mario Ghossoub & David Saunders, 2020. "On the Continuity of the Feasible Set Mapping in Optimal Transport," Papers 2009.12838, arXiv.org.
    2. Alfred Galichon & Robert McCann, 2019. "Special Issue: Optimal Transportation, Equilibrium, and Applications to Economics," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 67(2), pages 345-347, March.

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    More about this item

    Keywords

    Matching under transferable utility; Hedonic pricing; Optimal transport; Multi-marginal problems; Purity; Uniqueness;
    All these keywords.

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

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