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

O'Callaghan, Patrick (2016): Parametric continuity from preferences when the topology is weak and actions are discrete.

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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.

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