Axioms for parametric continuity of utility when the topology is coarse
Autor: | Patrick O'Callaghan |
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Rok vydání: | 2017 |
Předmět: |
Economics and Econometrics
Closed set Function space Computer science Applied Mathematics Discrete space 010102 general mathematics 05 social sciences Disjoint sets Topology 01 natural sciences Metrization theorem 0502 economics and business Product topology 0101 mathematics Axiom Topology (chemistry) 050205 econometrics |
Zdroj: | Journal of Mathematical Economics. 72:88-94 |
ISSN: | 0304-4068 |
Popis: | In economics we often take as primitive a collection of preference orderings (on actions or alternatives) indexed by a parameter. Moreover, it is often useful to represent such preferences with a collection of utility functions that is continuous in the parameter. Existing representation theorems assume that the topology on the parameter space is metrizable. This excludes settings where the topology is coarse e.g. the weak ∗ topology on a set of probability measures or the product topology on many function spaces. Yet such spaces are often normal (disjoint closed sets can be separated). We introduce an axiom on preferences for parametric continuity when actions are countable and the parameter space is normal. Utility is jointly continuous on actions × parameters when actions have the discrete topology. |
Databáze: | OpenAIRE |
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