IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/96108.html
   My bibliography  Save this paper

Savage's theorem with atoms

Author

Listed:
  • Ha-Huy, Thai

Abstract

The famous theorem of Savage is based on the richness of the states space, by assuming a 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 atom swarming condition. Applications for the establishment of an inter-temporal evaluation a la Koopman, and for the configuration under unlikely atoms of Mackenzie Mackenzie2018 are provided.

Suggested Citation

  • Ha-Huy, Thai, 2019. "Savage's theorem with atoms," MPRA Paper 96108, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:96108
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/96108/1/MPRA_paper_96108.pdf
    File Function: original version
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    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.
    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. Johanna Etner & Meglena Jeleva & Jean-Marc Tallon, 2009. "Decision theory under uncertainty," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00429573, HAL.
    16. 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.
    17. Kopylov, Igor, 2010. "Simple axioms for countably additive subjective probability," Journal of Mathematical Economics, Elsevier, vol. 46(5), pages 867-876, September.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Stanca, Lorenzo, 2020. "A simplified approach to subjective expected utility," Journal of Mathematical Economics, Elsevier, vol. 87(C), pages 151-160.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Mackenzie, Andrew, 2019. "A foundation for probabilistic beliefs with or without atoms," Theoretical Economics, Econometric Society, vol. 14(2), May.
    2. Konstantinos Georgalos, 2019. "An experimental test of the predictive power of dynamic ambiguity models," Journal of Risk and Uncertainty, Springer, vol. 59(1), pages 51-83, August.
    3. Adam Dominiak & Jean-Philippe Lefort, 2021. "Ambiguity and Probabilistic Information," Management Science, INFORMS, vol. 67(7), pages 4310-4326, July.
    4. Klaus Nehring, 2006. "Decision-Making in the Context of Imprecise Probabilistic Beliefs," Economics Working Papers 0034, Institute for Advanced Study, School of Social Science.
    5. Amit Kothiyal & Vitalie Spinu & Peter Wakker, 2014. "An experimental test of prospect theory for predicting choice under ambiguity," Journal of Risk and Uncertainty, Springer, vol. 48(1), pages 1-17, February.
    6. Federica Ceron & Vassili Vergopoulos, 2020. "Recursive objective and subjective multiple priors," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-02563318, HAL.
    7. Simone Cerreia-Vioglio & Paolo Ghirardato & Fabio Maccheroni & Massimo Marinacci & Marciano Siniscalchi, 2011. "Rational preferences under ambiguity," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 48(2), pages 341-375, October.
    8. Qu, Xiangyu, 2013. "Maxmin expected utility with additivity on unambiguous events," Journal of Mathematical Economics, Elsevier, vol. 49(3), pages 245-249.
    9. Siniscalchi, Marciano, 2006. "A behavioral characterization of plausible priors," Journal of Economic Theory, Elsevier, vol. 128(1), pages 91-135, May.
    10. Pahlke, Marieke, 2022. "Dynamic consistency in incomplete information games with multiple priors," Games and Economic Behavior, Elsevier, vol. 133(C), pages 85-108.
    11. Petturiti, Davide & Vantaggi, Barbara, 2024. "The impact of ambiguity on dynamic portfolio selection in the epsilon-contaminated binomial market model," European Journal of Operational Research, Elsevier, vol. 314(3), pages 1029-1039.
    12. Tommi Ekholm & Erin Baker, 2022. "Multiple Beliefs, Dominance and Dynamic Consistency," Management Science, INFORMS, vol. 68(1), pages 529-540, January.
    13. Fujii, Tomoki, 2017. "Dynamic Poverty Decomposition Analysis: An Application to the Philippines," World Development, Elsevier, vol. 100(C), pages 69-84.
    14. Georgalos, Konstantinos, 2021. "Dynamic decision making under ambiguity: An experimental investigation," Games and Economic Behavior, Elsevier, vol. 127(C), pages 28-46.
    15. Geoffrey Heal & Antony Millner, 2013. "Uncertainty and decision in climate change economics," GRI Working Papers 108, Grantham Research Institute on Climate Change and the Environment.
    16. Abdellaoui, Mohammed & Wakker, Peter P., 2020. "Savage for dummies and experts," Journal of Economic Theory, Elsevier, vol. 186(C).
    17. Lorenzo Bastianello & Vassili Vergopoulos, 2024. "Discounted Subjective Expected Utility in Continuous Time," Papers 2403.15319, arXiv.org.
    18. Gumen, Anna & Savochkin, Andrei, 2013. "Dynamically stable preferences," Journal of Economic Theory, Elsevier, vol. 148(4), pages 1487-1508.
    19. Helena Gaspars-Wieloch, 2015. "On a decision rule supported by a forecasting stage based on the decision maker’s coefficient of optimism," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 23(3), pages 579-594, September.
    20. Ceron, Federica & Vergopoulos, Vassili, 2022. "Objective rationality and recursive multiple priors," Journal of Mathematical Economics, Elsevier, vol. 102(C).

    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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:pra:mprapa:96108. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Joachim Winter (email available below). General contact details of provider: https://edirc.repec.org/data/vfmunde.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.