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On the continuity of the feasible set mapping in optimal transport

Author

Listed:
  • Mario Ghossoub

    (University of Waterloo)

  • David Saunders

    (University of Waterloo)

Abstract

Consider the set of probability measures with given marginal distributions on the product of two complete, separable metric spaces, seen as a correspondence when the marginal distributions vary. Bergin (Econ Theory 13: 471–481, 1999) established the continuity of this correspondence, and in this note, we present a novel and considerably shorter proof of this important result.

Suggested Citation

  • Mario Ghossoub & David Saunders, 2021. "On the continuity of the feasible set mapping in optimal transport," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 9(1), pages 113-117, April.
    • Handle: RePEc:spr:etbull:v:9:y:2021:i:1:d:10.1007_s40505-021-00199-8
    DOI: 10.1007/s40505-021-00199-8
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    References listed on IDEAS

    as
    1. Alfred Galichon, 2016. "Optimal Transport Methods in Economics," Economics Books, Princeton University Press, edition 1, number 10870.
    2. M. Zarichnyi, 2002. "Correspondences of probability measures with restricted marginals revisited," GE, Growth, Math methods 0210006, University Library of Munich, Germany.
    3. James Bergin, 1999. "On the continuity of correspondences on sets of measures with restricted marginals," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 13(2), pages 471-481.
    4. Alfred Galichon, 2016. "Optimal transport methods in economics," Post-Print hal-03256830, HAL.
    Full references (including those not matched with items on IDEAS)

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    Cited by:

    1. Dirk Bergemann & Tan Gan & Yingkai Li, 2023. "Managing Persuasion Robustly: The Optimality of Quota Rules," Papers 2310.10024, arXiv.org.

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    More about this item

    Keywords

    Optimal transport; Measures on product spaces with fixed marginals; Continuity of correspondences on spaces of measures;
    All these keywords.

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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