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On the Continuity of the Feasible Set Mapping in Optimal Transport

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  • Mario Ghossoub
  • David Saunders

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. In problems of optimal transport, continuity of this correspondence from marginal to joint distributions is often desired, in light of Berge's Maximum Theorem, to establish continuity of the value function in the marginal distributions, as well as stability of the set of optimal transport plans. Bergin (1999) established the continuity of this correspondence, and in this note, we present a novel and considerably shorter proof of this important result. We then examine an application to an assignment game (transferable utility matching problem) with unknown type distributions.

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  • Mario Ghossoub & David Saunders, 2020. "On the Continuity of the Feasible Set Mapping in Optimal Transport," Papers 2009.12838, arXiv.org.
    • Handle: RePEc:arx:papers:2009.12838
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    References listed on IDEAS

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    1. Alfred Galichon, 2016. "Optimal Transport Methods in Economics," Economics Books, Princeton University Press, edition 1, number 10870.
    2. 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.
    3. 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.
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    5. 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.
    6. Alfred Galichon, 2016. "Optimal transport methods in economics," Post-Print hal-03256830, HAL.
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