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The Nonlinear Bernstein-Schrödinger Equation in Economics

Author

Listed:
  • Alfred Galichon

    (ECON - Département d'économie (Sciences Po) - Sciences Po - Sciences Po - CNRS - Centre National de la Recherche Scientifique)

  • Scott Kominers

    (Harvard University)

  • Simon Weber

    (ECON - Département d'économie (Sciences Po) - Sciences Po - Sciences Po - CNRS - Centre National de la Recherche Scientifique)

Abstract

In this paper we relate the Equilibrium Assignment Problem (EAP), which is underlying in several economics models, to a system of nonlinear equations that we call the "nonlinear Bernstein-Schrödinger system", which is well-known in the linear case, but whose nonlinear extension does not seem to have been studied. We apply this connection to derive an existence result for the EAP, and an efficient computational method.

Suggested Citation

  • Alfred Galichon & Scott Kominers & Simon Weber, 2015. "The Nonlinear Bernstein-Schrödinger Equation in Economics," SciencePo Working papers Main hal-03393000, HAL.
    • Handle: RePEc:hal:spmain:hal-03393000
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    References listed on IDEAS

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    1. repec:hal:spmain:info:hdl:2441/5kmb4ke32h9ur9159sab6hvkck is not listed on IDEAS
    2. Alfred Galichon & Scott Kominers & Simon Weber, 2014. "An Empirical Framework for Matching with Imperfectly Transferable Utility," Working Papers hal-03460155, HAL.
    3. Becker, Gary S, 1973. "A Theory of Marriage: Part I," Journal of Political Economy, University of Chicago Press, vol. 81(4), pages 813-846, July-Aug..
    4. Eugene Choo & Aloysius Siow, 2006. "Who Marries Whom and Why," Journal of Political Economy, University of Chicago Press, vol. 114(1), pages 175-201, February.
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    Cited by:

    1. Doorley, Karina & Dupuy, Arnaud & Weber, Simon, 2019. "The empirical content of marital surplus in matching models," Economics Letters, Elsevier, vol. 176(C), pages 51-54.
    2. Bisin, Alberto & Tura, Giulia, 2019. "Marriage, Fertility, and Cultural Integration in Italy," CEPR Discussion Papers 14179, C.E.P.R. Discussion Papers.
    3. Montacer Essid & Michele Pavon, 2019. "Traversing the Schrödinger Bridge Strait: Robert Fortet’s Marvelous Proof Redux," Journal of Optimization Theory and Applications, Springer, vol. 181(1), pages 23-60, April.
    4. Liang Chen & Eugene Choo & Alfred Galichon & Simon Weber, 2021. "Matching Function Equilibria with Partial Assignment: Existence, Uniqueness and Estimation," Papers 2102.02071, arXiv.org, revised Sep 2023.
    5. Alberto Bisin & Giulia Tura, 2019. "Marriage, Fertility, and Cultural Integration of Immigrants in Italy," Working Papers 2019-063, Human Capital and Economic Opportunity Working Group.

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