IDEAS home Printed from https://ideas.repec.org/a/kap/theord/v73y2012i4p591-604.html
   My bibliography  Save this article

Expanding state space and extension of beliefs

Author

Listed:
  • Takashi Hayashi

Abstract

This article provides a simple decision theoretic model in which elements of the world successively enter the decision maker’s scope and the state space expands over time, which is intended to be the closest correspondence to the standard subjective expected utility theory. We propose a dynamic consistency condition that after any expansion of the scope, the preference ranking should remain unchanged over acts to which the expansion is irrelevant. Together with other natural axioms, it characterizes a model in which the decision maker’s belief extends over time in order that the marginal distribution of the new belief induced over the old state space coincides with the old belief. It is extended to encompass both expansion of scope and learning events, and we characterize the model with an additional property that the decision maker’s belief updating follows Bayes’ rule when she learns events. Copyright Springer Science+Business Media New York 2012

Suggested Citation

  • Takashi Hayashi, 2012. "Expanding state space and extension of beliefs," Theory and Decision, Springer, vol. 73(4), pages 591-604, October.
    • Handle: RePEc:kap:theord:v:73:y:2012:i:4:p:591-604
    DOI: 10.1007/s11238-012-9302-y
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s11238-012-9302-y
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s11238-012-9302-y?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 search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. Simon Grant & John Quiggin, 2008. "Bounded rationality and small worlds," Risk & Uncertainty Working Papers WPR08_2, Risk and Sustainable Management Group, University of Queensland.
    3. Costis Skiadas, 1997. "Conditioning and Aggregation of Preferences," Econometrica, Econometric Society, vol. 65(2), pages 347-368, March.
    4. Epstein Larry G. & Le Breton Michel, 1993. "Dynamically Consistent Beliefs Must Be Bayesian," Journal of Economic Theory, Elsevier, vol. 61(1), pages 1-22, October.
    5. Dekel, Eddie & Lipman, Barton L. & Rustichini, Aldo, 1998. "Recent developments in modeling unforeseen contingencies," European Economic Review, Elsevier, vol. 42(3-5), pages 523-542, May.
    6. Kim-Sau Chung & Oliver Board, 2007. "Object-Based Unawareness," Working Papers 2007-2, University of Minnesota, Department of Economics, revised 24 Aug 2007.
    7. Heifetz, Aviad & Meier, Martin & Schipper, Burkhard C., 2006. "Interactive unawareness," Journal of Economic Theory, Elsevier, vol. 130(1), pages 78-94, September.
    8. Li, Jing, 2009. "Information structures with unawareness," Journal of Economic Theory, Elsevier, vol. 144(3), pages 977-993, May.
    9. Eddie Dekel & Barton L. Lipman & Aldo Rustichini, 1998. "Standard State-Space Models Preclude Unawareness," Econometrica, Econometric Society, vol. 66(1), pages 159-174, January.
    10. Paolo Ghirardato, 2002. "Revisiting Savage in a conditional world," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 20(1), pages 83-92.
    11. David S. Ahn & Haluk Ergin, 2010. "Framing Contingencies," Econometrica, Econometric Society, vol. 78(2), pages 655-695, March.
    12. , G. & , & ,, 2007. "Coarse contingencies and ambiguity," Theoretical Economics, Econometric Society, vol. 2(4), December.
    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. Burkhard C. Schipper, 2024. "Predicting the Unpredictable under Subjective Expected Utility," Papers 2403.01421, arXiv.org.
    2. Ekaterina Svetlova & Henk van Elst, 2012. "How is non-knowledge represented in economic theory?," Papers 1209.2204, arXiv.org.
    3. Adam Dominiak & Ani Guerdjikova, 2021. "Pessimism and optimism towards new discoveries," Theory and Decision, Springer, vol. 90(3), pages 321-370, May.
    4. Dominiak, Adam & Tserenjigmid, Gerelt, 2022. "Ambiguity under growing awareness," Journal of Economic Theory, Elsevier, vol. 199(C).
    5. 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.

    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. Burkhard Schipper, 2010. "Revealed Unawareness," Working Papers 303, University of California, Davis, Department of Economics.
    2. Kochov, Asen, 2018. "A behavioral definition of unforeseen contingencies," Journal of Economic Theory, Elsevier, vol. 175(C), pages 265-290.
    3. Dominiak, Adam & Tserenjigmid, Gerelt, 2022. "Ambiguity under growing awareness," Journal of Economic Theory, Elsevier, vol. 199(C).
    4. 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.
    5. Burkhard Schipper, 2013. "Awareness-dependent subjective expected utility," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(3), pages 725-753, August.
    6. Zhao, Xiaojian, 2011. "Framing contingencies in contracts," Mathematical Social Sciences, Elsevier, vol. 61(1), pages 31-40, January.
    7. Spyros Galanis, 2013. "Unawareness of theorems," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 52(1), pages 41-73, January.
    8. Fiorini, Luciana C. & Rodrigues-Neto, José A., 2017. "Self-consistency, consistency and cycles in non-partitional knowledge models," Mathematical Social Sciences, Elsevier, vol. 87(C), pages 11-21.
    9. Auster, Sarah, 2013. "Asymmetric awareness and moral hazard," Games and Economic Behavior, Elsevier, vol. 82(C), pages 503-521.
    10. Galanis, Spyros, 2018. "Speculation under unawareness," Games and Economic Behavior, Elsevier, vol. 109(C), pages 598-615.
    11. Schipper, Burkhard C, 2010. "Revealed Unawareness," MPRA Paper 21491, University Library of Munich, Germany.
    12. Blume, Andreas & Gneezy, Uri, 2010. "Cognitive forward induction and coordination without common knowledge: An experimental study," Games and Economic Behavior, Elsevier, vol. 68(2), pages 488-511, March.
    13. Sarah Auster, 2012. "Asymmetric Awareness and Moral Hazard," Economics Working Papers ECO2012/23, European University Institute.
    14. 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.
    15. Minardi, Stefania & Savochkin, Andrei, 2019. "Subjective contingencies and limited Bayesian updating," Journal of Economic Theory, Elsevier, vol. 183(C), pages 1-45.
    16. Spyros Galanis, 2011. "Syntactic foundations for unawareness of theorems," Theory and Decision, Springer, vol. 71(4), pages 593-614, October.
    17. Schipper, Burkhard C, 2011. "Preference-Based Unawareness," MPRA Paper 30221, University Library of Munich, Germany.
    18. Dietrich, Franz, 2018. "Savage's theorem under changing awareness," Journal of Economic Theory, Elsevier, vol. 176(C), pages 1-54.
    19. Sarah Auster, 2011. "Asymmetric Awareness and Moral Hazard," Economics Working Papers ECO2011/, European University Institute.
    20. Chakravarty, Surajeet & Kelsey, David & Teitelbaum, Joshua C., 2022. "Reverse Bayesianism and act independence," Journal of Economic Theory, Elsevier, vol. 203(C).

    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:kap:theord:v:73:y:2012:i:4:p:591-604. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.