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

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  • Pierre-André Chiappori

    ()

  • Robert McCann

    ()

  • Lars Nesheim

    ()

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.
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Suggested Citation

  • 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.
  • Handle: RePEc:spr:joecth:v:42:y:2010:i:2:p:317-354 DOI: 10.1007/s00199-009-0455-z
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    References listed on IDEAS

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    1. Neil E. Gretsky & Joseph M. Ostroy & William R. Zame, 1990. "The Nonatomic Assignment Model," UCLA Economics Working Papers 605, UCLA Department of Economics.
    2. Gretsky, Neil E & Ostroy, Joseph M & Zame, William R, 1992. "The Nonatomic Assignment Model," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 2(1), pages 103-127, January.
    3. repec:dau:papers:123456789/6443 is not listed on IDEAS
    4. Roth, Alvin E. & Sotomayor, Marilda, 1992. "Two-sided matching," Handbook of Game Theory with Economic Applications,in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 16, pages 485-541 Elsevier.
    5. James Heckman & Rosa Matzkin & Lars Nesheim, 2005. "Nonparametric estimation of nonadditive hedonic models," CeMMAP working papers CWP03/05, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    6. Gretsky, Neil E. & Ostroy, Joseph M. & Zame, William R., 1999. "Perfect Competition in the Continuous Assignment Model," Journal of Economic Theory, Elsevier, vol. 88(1), pages 60-118, September.
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    More about this item

    Keywords

    Hedonic price equilibrium; Matching; Optimal transportation; Spence-Mirrlees condition; Monge–Kantorovich; Twist condition; C62; C78; D50;

    JEL classification:

    • G18 - Financial Economics - - General Financial Markets - - - Government Policy and Regulation

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