IDEAS home Printed from https://ideas.repec.org/a/eee/jetheo/v176y2018icp1-54.html
   My bibliography  Save this article

Savage's theorem under changing awareness

Author

Listed:
  • Dietrich, Franz

Abstract

This paper proposes a simple unified framework of choice under changing awareness, addressing both outcome awareness and (nature) state awareness, and both how fine and how exhaustive the awareness is. Six axioms characterize an (essentially unique) expected-utility rationalization of preferences, in which utilities and probabilities are revised according to three revision rules when awareness changes: (R1) utilities of unaffected outcomes are transformed affinely; (R2) probabilities of unaffected events are transformed proportionally; (R3) enough probabilities ‘objectively’ never change (they represent revealed objective risk). Savage's Theorem is a special case of the theorem, namely the special case of fixed awareness, in which our axioms reduce to Savage's axioms while R1 and R2 hold trivially and R3 reduces to Savage's requirement of atomless probabilities. Rule R2 parallels Karni and Viero's (2013) ‘reverse Bayesianism’ and Ahn and Ergin's (2010) ‘partition-dependence’. The theorem draws mathematically on Kopylov (2007), Niiniluoto (1972) and Wakker (1981).

Suggested Citation

  • Dietrich, Franz, 2018. "Savage's theorem under changing awareness," Journal of Economic Theory, Elsevier, vol. 176(C), pages 1-54.
    • Handle: RePEc:eee:jetheo:v:176:y:2018:i:c:p:1-54
    DOI: 10.1016/j.jet.2018.01.015
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0022053118300231
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jet.2018.01.015?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Dietrich, Franz & List, Christian, 2016. "Reason-Based Choice And Context-Dependence: An Explanatory Framework," Economics and Philosophy, Cambridge University Press, vol. 32(2), pages 175-229, July.
    2. Edi Karni & Marie-Louise Vier?, 2013. ""Reverse Bayesianism": A Choice-Based Theory of Growing Awareness," American Economic Review, American Economic Association, vol. 103(7), pages 2790-2810, December.
    3. repec:hal:pseose:halshs-01249514 is not listed on IDEAS
    4. Kopylov, Igor, 2007. "Subjective probabilities on "small" domains," Journal of Economic Theory, Elsevier, vol. 133(1), pages 236-265, March.
    5. repec:hal:wpaper:halshs-01249632 is not listed on IDEAS
    6. Dietrich, Franz & List, Christian, 2016. "Mentalism Versus Behaviourism In Economics: A Philosophy-Of-Science Perspective," Economics and Philosophy, Cambridge University Press, vol. 32(2), pages 249-281, July.
    7. Heifetz, Aviad & Meier, Martin & Schipper, Burkhard C., 2006. "Interactive unawareness," Journal of Economic Theory, Elsevier, vol. 130(1), pages 78-94, September.
    8. Burkhard Schipper, 2013. "Awareness-dependent subjective expected utility," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(3), pages 725-753, August.
    9. Halpern, Joseph Y., 2001. "Alternative Semantics for Unawareness," Games and Economic Behavior, Elsevier, vol. 37(2), pages 321-339, November.
    10. Eddie Dekel & Barton L. Lipman & Aldo Rustichini, 1998. "Standard State-Space Models Preclude Unawareness," Econometrica, Econometric Society, vol. 66(1), pages 159-174, January.
    11. Brian Hill, 2010. "Awareness Dynamics," Post-Print hal-00521801, HAL.
    12. Karni, Edi & Vierø, Marie-Louise, 2017. "Awareness of unawareness: A theory of decision making in the face of ignorance," Journal of Economic Theory, Elsevier, vol. 168(C), pages 301-328.
    13. Halpern, Joseph Y. & Rego, Leandro Chaves, 2008. "Interactive unawareness revisited," Games and Economic Behavior, Elsevier, vol. 62(1), pages 232-262, January.
    14. David S. Ahn & Haluk Ergin, 2010. "Framing Contingencies," Econometrica, Econometric Society, vol. 78(2), pages 655-695, March.
    15. repec:hal:pseose:halshs-01249632 is not listed on IDEAS
    16. Karni, Edi & Schmeidler, David, 1991. "Utility theory with uncertainty," Handbook of Mathematical Economics, in: W. Hildenbrand & H. Sonnenschein (ed.), Handbook of Mathematical Economics, edition 1, volume 4, chapter 33, pages 1763-1831, Elsevier.
    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. Dietrich, Franz, 2021. "Fully Bayesian aggregation," Journal of Economic Theory, Elsevier, vol. 194(C).
    2. Grant Simon & Guerdjikova Ani & Quiggin John, 2021. "Ambiguity and Awareness: A Coherent Multiple Priors Model," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 21(2), pages 571-612, June.
    3. Christoph K. Becker & Tigran Melkonyan & Eugenio Proto & Andis Sofianos & Stefan T. Trautmann, 2020. "Reverse Bayesianism: Revising Beliefs in Light of Unforeseen Events," CESifo Working Paper Series 8662, CESifo.
    4. Adam Dominiak & Ani Guerdjikova, 2021. "Pessimism and optimism towards new discoveries," Theory and Decision, Springer, vol. 90(3), pages 321-370, May.
    5. Vierø, Marie-Louise, 2021. "An intertemporal model of growing awareness," Journal of Economic Theory, Elsevier, vol. 197(C).
    6. Boissonnet, Niels & Ghersengorin, Alexis & Gleyze, Simon, 2020. "Revealed Deliberate Preference Changes," MPRA Paper 101756, University Library of Munich, Germany.
    7. Dominiak, Adam & Tserenjigmid, Gerelt, 2022. "Ambiguity under growing awareness," Journal of Economic Theory, Elsevier, vol. 199(C).
    8. Burkhard C. Schipper, 2024. "Predicting the Unpredictable under Subjective Expected Utility," Papers 2403.01421, arXiv.org.
    9. Marcus Pivato, 2020. "Subjective expected utility with a spectral state space," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 69(2), pages 249-313, March.
    10. Abdellaoui, Mohammed & Wakker, Peter P., 2020. "Savage for dummies and experts," Journal of Economic Theory, Elsevier, vol. 186(C).

    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. Karni, Edi & Vierø, Marie-Louise, 2017. "Awareness of unawareness: A theory of decision making in the face of ignorance," Journal of Economic Theory, Elsevier, vol. 168(C), pages 301-328.
    2. Dominiak, Adam & Tserenjigmid, Gerelt, 2022. "Ambiguity under growing awareness," Journal of Economic Theory, Elsevier, vol. 199(C).
    3. Edi Karni & Marie-Louise Vier?, 2013. ""Reverse Bayesianism": A Choice-Based Theory of Growing Awareness," American Economic Review, American Economic Association, vol. 103(7), pages 2790-2810, December.
    4. Becker, Christoph K. & Melkonyan, Tigran & Proto, Eugenio & Sofianos, Andis & Trautmann, Stefan T., 2020. "Reverse Bayesianism: Revising Beliefs in Light of Unforeseen Events," IZA Discussion Papers 13821, Institute of Labor Economics (IZA).
    5. Chakravarty, Surajeet & Kelsey, David & Teitelbaum, Joshua C., 2022. "Reverse Bayesianism and act independence," Journal of Economic Theory, Elsevier, vol. 203(C).
    6. Gaia Belardinelli & Burkhard C. Schipper, 2023. "Implicit Knowledge in Unawareness Structures," Working Papers 360, University of California, Davis, Department of Economics.
    7. Burkhard Schipper, 2013. "Awareness-dependent subjective expected utility," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(3), pages 725-753, August.
    8. Pintér, Miklós & Udvari, Zsolt, 2011. "Generalized type spaces," MPRA Paper 34107, University Library of Munich, Germany.
    9. Kochov, Asen, 2018. "A behavioral definition of unforeseen contingencies," Journal of Economic Theory, Elsevier, vol. 175(C), pages 265-290.
    10. Burkhard Schipper, 2010. "Revealed Unawareness," Working Papers 303, University of California, Davis, Department of Economics.
    11. Schipper, Burkhard C, 2011. "Preference-Based Unawareness," MPRA Paper 30221, University Library of Munich, Germany.
    12. Burkhard Schipper, 2011. "Preference-Dependent Unawareness," Working Papers 269, University of California, Davis, Department of Economics.
    13. Burkhard C. Schipper, 2024. "Predicting the Unpredictable under Subjective Expected Utility," Papers 2403.01421, arXiv.org.
    14. Konrad Grabiszewski, 2015. "Rationalizing epistemic bounded rationality," Theory and Decision, Springer, vol. 78(4), pages 629-637, April.
    15. Heinsalu, Sander, 2014. "Universal type structures with unawareness," Games and Economic Behavior, Elsevier, vol. 83(C), pages 255-266.
    16. Oliver Walker, 2011. "Unawareness with �possible� possible worlds," GRI Working Papers 69, Grantham Research Institute on Climate Change and the Environment.
    17. Fukuda, Satoshi, 2021. "Unawareness without AU Introspection," Journal of Mathematical Economics, Elsevier, vol. 94(C).
    18. Martin Meier & Burkhard Schipper, 2014. "Bayesian games with unawareness and unawareness perfection," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 56(2), pages 219-249, June.
    19. Ani Guerdjikova & John Quiggin, 2018. "Intertemporal Portfolio Choice with Incorrect Beliefs and Aversion to Surprise," Post-Print hal-02086151, HAL.
    20. Marcus Pivato, 2020. "Subjective expected utility with a spectral state space," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 69(2), pages 249-313, March.

    More about this item

    Keywords

    Decision under uncertainty; Outcome unawareness versus state unawareness; Non-fine versus non-exhaustive awareness; Utility revision versus probability revision; Small worlds versus grand worlds;
    All these keywords.

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

    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:eee:jetheo:v:176:y:2018:i:c:p:1-54. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/622869 .

    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.