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On the continuity of correspondences on sets of measures with restricted marginals

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  • James Bergin

    (Department of Economics, Queen's University, Kingston, Ontario, K7L 3N6, CANADA)

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.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joecth:v:13:y:1999:i:2:p:471-481
    Note: Received: April 23, 1997; revised version: January 16, 1998
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    References listed on IDEAS

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    1. 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.
    2. Jovanovic, Boyan & Rosenthal, Robert W., 1988. "Anonymous sequential games," Journal of Mathematical Economics, Elsevier, vol. 17(1), pages 77-87, February.
    3. Bergin, James & Bernhardt, Dan, 1992. "Anonymous sequential games with aggregate uncertainty," Journal of Mathematical Economics, Elsevier, vol. 21(6), pages 543-562.
    4. Jovanovic, Boyan, 1982. "Selection and the Evolution of Industry," Econometrica, Econometric Society, vol. 50(3), pages 649-670, May.
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    Cited by:

    1. 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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    More about this item

    Keywords

    Measures on product spaces with restricted marginals · Continuity of correspondences on spaces of measures.;

    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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