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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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    1. Johanna Etner & Meglena Jeleva & Jean‐Marc Tallon, 2012. "Decision Theory Under Ambiguity," Journal of Economic Surveys, Wiley Blackwell, vol. 26(2), pages 234-270, April.
    2. Kopylov, Igor, 2007. "Subjective probabilities on "small" domains," Journal of Economic Theory, Elsevier, vol. 133(1), pages 236-265, March.
    3. Mackenzie, Andrew, 2019. "A foundation for probabilistic beliefs with or without atoms," Theoretical Economics, Econometric Society, vol. 14(2), May.
    4. Gilboa Itzhak & Schmeidler David, 1993. "Updating Ambiguous Beliefs," Journal of Economic Theory, Elsevier, vol. 59(1), pages 33-49, February.
    5. Gilboa,Itzhak, 2009. "Theory of Decision under Uncertainty," Cambridge Books, Cambridge University Press, number 9780521517324, January.
    6. Itzhak Gilboa & Fabio Maccheroni & Massimo Marinacci & David Schmeidler, 2010. "Objective and Subjective Rationality in a Multiple Prior Model," Econometrica, Econometric Society, vol. 78(2), pages 755-770, March.
    7. José Luis Montiel Olea & Tomasz Strzalecki, 2014. "Axiomatization and Measurement of Quasi-Hyperbolic Discounting," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 129(3), pages 1449-1499.
    8. Paolo Ghirardato & Fabio Maccheroni & Massimo Marinacci & Marciano Siniscalchi, 2003. "A Subjective Spin on Roulette Wheels," Econometrica, Econometric Society, vol. 71(6), pages 1897-1908, November.
    9. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    10. David Laibson, 1997. "Golden Eggs and Hyperbolic Discounting," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 112(2), pages 443-478.
    11. Machina, Mark J & Schmeidler, David, 1992. "A More Robust Definition of Subjective Probability," Econometrica, Econometric Society, vol. 60(4), pages 745-780, July.
    12. Peter Wakker, 1993. "Savage's Axioms Usually Imply Violation of Strict Stochastic Dominance," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 60(2), pages 487-493.
    13. repec:hal:pseose:halshs-00643580 is not listed on IDEAS
    14. Chateauneuf, Alain, 1985. "On the existence of a probability measure compatible with a total preorder on a Boolean algebra," Journal of Mathematical Economics, Elsevier, vol. 14(1), pages 43-52, February.
    15. Wakker, Peter P. & Zank, Horst, 1999. "A unified derivation of classical subjective expected utility models through cardinal utility," Journal of Mathematical Economics, Elsevier, vol. 32(1), pages 1-19, August.
    16. Kopylov, Igor, 2010. "Simple axioms for countably additive subjective probability," Journal of Mathematical Economics, Elsevier, vol. 46(5), pages 867-876, September.
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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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