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Parametric continuity from preferences when the topology is weak and actions are discrete

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  • O'Callaghan, Patrick

Abstract

Empirical settings often involve discrete actions and rich parameter spaces where the notion of open set is constrained. This restricts the class of continuous functions from parameters to actions. Yet suitably continuous policies and value functions are necessary for many standard results in economic theory. We derive these tools from preferences when the parameter space is normal (disjoint closed sets can be separated). Whereas we use preferences to generate an endogenous pseudometric, existing results require metrizable parameter spaces. Still, weakly ordered parameters do not form a normal space. We provide a solution and close with an algorithm for eliciting preferences.

Suggested Citation

  • O'Callaghan, Patrick, 2016. "Parametric continuity from preferences when the topology is weak and actions are discrete," MPRA Paper 72356, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:72356
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    File URL: https://mpra.ub.uni-muenchen.de/72356/1/MPRA_paper_72356.pdf
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    References listed on IDEAS

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    More about this item

    Keywords

    Continuity; preferences; metrizability;
    All these keywords.

    JEL classification:

    • C0 - Mathematical and Quantitative Methods - - General
    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling

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