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Savage's theorem with atoms

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  • Ha-Huy, Thai

Abstract

The famous theorem of Savage is based on the richness of the states space, by assuming a \textit{continuum} nature for this set. In order to fill the gap, this article considers Savage's theorem with discrete state space. The article points out the importance the existence of pair event in the existence of utility function and the subjective probability. Under the discrete states space, this can be ensured by the intuitive \textit{atom swarming} condition. Applications for the establishment of an inter-temporal evaluation \emph{\`a la } Koopman \cite{K60}, \cite{K72}, and for the configuration under \textit{unlikely atoms} of Mackenzie \cite{Mackenzie2018} are provided.

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  • Ha-Huy, Thai, 2019. "Savage's theorem with atoms," MPRA Paper 94516, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:94516
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    References listed on IDEAS

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    Cited by:

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    More about this item

    Keywords

    Savage theorem; Koopman representation; expected utility function; atom swarming.;
    All these keywords.

    JEL classification:

    • C00 - Mathematical and Quantitative Methods - - General - - - General
    • D10 - Microeconomics - - Household Behavior - - - General
    • D90 - Microeconomics - - Micro-Based Behavioral Economics - - - General

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