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

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Author Info
James Bergin

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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 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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File URL: http://www.econ.queensu.ca/working_papers/papers/qed_wp_959.pdf
File Format: application/pdf
File Function: First version 1997
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Publisher Info
Paper provided by Queen's University, Department of Economics in its series Working Papers with number 959.

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Date of creation: Nov 1997
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Handle: RePEc:qed:wpaper:959

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Related research
Keywords: Optimization; Measure Spaces;

Find related papers by JEL classification:
C6 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming
C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory

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