On the continuity of the feasible set mapping in optimal transport

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.

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Correspondence to David Saunders.

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Mario Ghossoub and David Saunders acknowledge financial support from the Natural Sciences and Engineering Research Council of Canada in the form of Discovery Grants (NSERC Grant Nos. 2018-03961 and 2017-04220 respectively).

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Ghossoub, M., Saunders, D. On the continuity of the feasible set mapping in optimal transport. Econ Theory Bull (2021). https://doi.org/10.1007/s40505-021-00199-8

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Keywords

  • Optimal transport
  • Measures on product spaces with fixed marginals
  • Continuity of correspondences on spaces of measures

JEL Classification

  • C60
  • C61