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On the Continuity of Correspondences on Sets of Measures with Restricted Marginals

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  • Bergin, James

Abstract

Consider the set of probability measures on a product space with the property that all have the same marginal distributions on the coordinate spaces. This set may be viewed as a correspondence, when the marginal distributions are varied. Here, it is shown that this correspondence is continuous. Numerous problems in economics involve optimization over a space of measures where one or more marginal distributions is given. Thus, for this class of problem, Berge's theorem of the maximum is applicable: the set of optimizers is upper-hemicontinuous and the value of the optimal solution varies with the parameters (marginals) continuously.
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Suggested Citation

  • Bergin, James, 1997. "On the Continuity of Correspondences on Sets of Measures with Restricted Marginals," Queen's Institute for Economic Research Discussion Papers 273393, Queen's University - Department of Economics.
    • Handle: RePEc:ags:queddp:273393
    DOI: 10.22004/ag.econ.273393
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    File URL: https://ageconsearch.umn.edu/record/273393/files/qed_wp_959.pdf
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    References listed on IDEAS

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    1. Bergin, James & Bernhardt, Dan, 1992. "Anonymous sequential games with aggregate uncertainty," Journal of Mathematical Economics, Elsevier, vol. 21(6), pages 543-562.
    2. Bergin, J & Bernhardt, D, 1995. "Anonymous Sequential Games: Existence and Characterization of Equilibria," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 5(3), pages 461-489, May.
    3. Jovanovic, Boyan, 1982. "Selection and the Evolution of Industry," Econometrica, Econometric Society, vol. 50(3), pages 649-670, May.
    4. Jovanovic, Boyan & Rosenthal, Robert W., 1988. "Anonymous sequential games," Journal of Mathematical Economics, Elsevier, vol. 17(1), pages 77-87, February.
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    2. 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.

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    Keywords

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    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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