IDEAS home Printed from https://ideas.repec.org/p/hal/journl/hal-03726359.html
   My bibliography  Save this paper

Ambiguity and Awareness: A Coherent Multiple Priors Model

Author

Listed:
  • Simon Grant

    (ANU - Australian National University, UQ [All campuses : Brisbane, Dutton Park Gatton, Herston, St Lucia and other locations] - The University of Queensland)

  • Ani Guerdjikova

    (GAEL - Laboratoire d'Economie Appliquée de Grenoble - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement - UGA - Université Grenoble Alpes - Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology - UGA - Université Grenoble Alpes)

  • John Quiggin

    (UQ [All campuses : Brisbane, Dutton Park Gatton, Herston, St Lucia and other locations] - The University of Queensland)

Abstract

Ambiguity in the ordinary language sense means that available information is open to multiple interpretations. We model this by assuming that individuals are unaware of some possibilities relevant to the outcome of their decisions and that multiple probabilities may arise over an individual's subjective state space depending on which of these possibilities are realized. We formalize a notion of coherent multiple priors and derive a representation result that with full awareness corresponds to the usual unique (Bayesian) prior but with less than full awareness generates multiple priors. When information is received with no change in awareness, each element of the set of priors is updated in the standard Bayesian fashion (that is, full Bayesian updating). An increase in awareness, however, leads to an expansion of the individual's subjective state and (in general) a contraction in the set of priors under consideration.

Suggested Citation

  • Simon Grant & Ani Guerdjikova & John Quiggin, 2021. "Ambiguity and Awareness: A Coherent Multiple Priors Model," Post-Print hal-03726359, HAL.
    • Handle: RePEc:hal:journl:hal-03726359
    DOI: 10.1515/bejte-2018-0185
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Alon, Shiri, 2015. "Worst-case expected utility," Journal of Mathematical Economics, Elsevier, vol. 60(C), pages 43-48.
    2. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
    3. John Quiggin, 2016. "The value of information and the value of awareness," Theory and Decision, Springer, vol. 80(2), pages 167-185, February.
    4. Simon Grant & John Quiggin, 2013. "Inductive reasoning about unawareness," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 54(3), pages 717-755, November.
    5. Anonymous, 2014. "Introduction to the Issue," Journal of Wine Economics, Cambridge University Press, vol. 9(1), pages 1-2, May.
    6. Ehud Lehrer & Roee Teper, 2014. "Extension Rules or What Would the Sage Do?," American Economic Journal: Microeconomics, American Economic Association, vol. 6(1), pages 5-22, February.
    7. Kochov, Asen, 2018. "A behavioral definition of unforeseen contingencies," Journal of Economic Theory, Elsevier, vol. 175(C), pages 265-290.
    8. Piermont, Evan, 2017. "Introspective unawareness and observable choice," Games and Economic Behavior, Elsevier, vol. 106(C), pages 134-152.
    9. Li, Jing, 2009. "Information structures with unawareness," Journal of Economic Theory, Elsevier, vol. 144(3), pages 977-993, May.
    10. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
    11. Cesaltina Pacheco Pires, 2002. "A Rule For Updating Ambiguous Beliefs," Theory and Decision, Springer, vol. 53(2), pages 137-152, September.
    12. Ghirardato, Paolo & Maccheroni, Fabio & Marinacci, Massimo, 2004. "Differentiating ambiguity and ambiguity attitude," Journal of Economic Theory, Elsevier, vol. 118(2), pages 133-173, October.
    13. Edi Karni & Marie-Louise Vierø, 2015. "Probabilistic sophistication and reverse Bayesianism," Journal of Risk and Uncertainty, Springer, vol. 50(3), pages 189-208, June.
    14. 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.
    15. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    16. Daniel Kahneman & Amos Tversky, 2013. "Prospect Theory: An Analysis of Decision Under Risk," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 6, pages 99-127, World Scientific Publishing Co. Pte. Ltd..
    17. Dietrich, Franz, 2018. "Savage's theorem under changing awareness," Journal of Economic Theory, Elsevier, vol. 176(C), pages 1-54.
    18. Heifetz, Aviad & Meier, Martin & Schipper, Burkhard C., 2006. "Interactive unawareness," Journal of Economic Theory, Elsevier, vol. 130(1), pages 78-94, September.
    19. Daniel Ellsberg, 1961. "Risk, Ambiguity, and the Savage Axioms," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 75(4), pages 643-669.
    20. Peter Klibanoff & Massimo Marinacci & Sujoy Mukerji, 2005. "A Smooth Model of Decision Making under Ambiguity," Econometrica, Econometric Society, vol. 73(6), pages 1849-1892, November.
    21. 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.
    22. Simon Grant & John Quiggin, 2015. "A preference model for choice subject to surprise," Theory and Decision, Springer, vol. 79(2), pages 167-180, September.
    23. Anonymous, 2014. "Introduction to the Issue," Journal of Wine Economics, Cambridge University Press, vol. 9(2), pages 109-110, August.
    24. Grant, Simon & Jude Kline, J. & Quiggin, John, 2018. "Contracting under uncertainty: A principal–agent model with ambiguity averse parties," Games and Economic Behavior, Elsevier, vol. 109(C), pages 582-597.
    25. Billot, Antoine & Vergopoulos, Vassili, 2018. "Expected utility without parsimony," Mathematical Social Sciences, Elsevier, vol. 93(C), pages 14-21.
    26. Viero, Marie-Louise, 2017. "An intertemporal model of growing awareness," Queen's Economics Department Working Papers 274714, Queen's University - Department of Economics.
    27. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    28. David S. Ahn & Haluk Ergin, 2010. "Framing Contingencies," Econometrica, Econometric Society, vol. 78(2), pages 655-695, March.
    29. Burkhard Schipper, 2014. "Unawareness - A Gentle Introduction to both the Literature and the Special Issue," Working Papers 145, University of California, Davis, Department of Economics.
    30. Burkhard Schipper, 2014. "Unawareness - A Gentle Introduction to both the Literature and the Special Issue," Working Papers 153, University of California, Davis, Department of Economics.
    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. Ani Guerdjikova & Jürgen Eichberger, 2023. "Cases and States ," Working Papers hal-03962412, HAL.
    2. Simon Grant & Idione Meneghel & Rabee Tourky, 2022. "Learning under unawareness," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 74(2), pages 447-475, September.

    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. Adam Dominiak & Ani Guerdjikova, 2021. "Pessimism and optimism towards new discoveries," Theory and Decision, Springer, vol. 90(3), pages 321-370, May.
    2. Dominiak, Adam & Tserenjigmid, Gerelt, 2022. "Ambiguity under growing awareness," Journal of Economic Theory, Elsevier, vol. 199(C).
    3. 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.
    4. Vierø, Marie-Louise, 2021. "An intertemporal model of growing awareness," Journal of Economic Theory, Elsevier, vol. 197(C).
    5. 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.
    6. Simon Dietz & Falk Niehörster, 2021. "Pricing ambiguity in catastrophe risk insurance," The Geneva Risk and Insurance Review, Palgrave Macmillan;International Association for the Study of Insurance Economics (The Geneva Association), vol. 46(2), pages 112-132, September.
    7. Dillenberger, David & Segal, Uzi, 2017. "Skewed noise," Journal of Economic Theory, Elsevier, vol. 169(C), pages 344-364.
    8. Zimper, Alexander, 2009. "Half empty, half full and why we can agree to disagree forever," Journal of Economic Behavior & Organization, Elsevier, vol. 71(2), pages 283-299, August.
    9. Dominiak, Adam & Tserenjigmid, Gerelt, 2018. "Belief consistency and invariant risk preferences," Journal of Mathematical Economics, Elsevier, vol. 79(C), pages 157-162.
    10. Burkhard C. Schipper, 2024. "Predicting the Unpredictable under Subjective Expected Utility," Papers 2403.01421, arXiv.org.
    11. Wenjun Ma & Burkhard C. Schipper, 2017. "Does exposure to unawareness affect risk preferences? A preliminary result," Theory and Decision, Springer, vol. 83(2), pages 245-257, August.
    12. Karni, Edi & Maccheroni, Fabio & Marinacci, Massimo, 2015. "Ambiguity and Nonexpected Utility," Handbook of Game Theory with Economic Applications,, Elsevier.
    13. Áron Tóbiás, 2023. "Cognitive limits and preferences for information," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 46(1), pages 221-253, June.
    14. Corina Birghila & Tim J. Boonen & Mario Ghossoub, 2023. "Optimal insurance under maxmin expected utility," Finance and Stochastics, Springer, vol. 27(2), pages 467-501, April.
    15. Massimiliano Amarante & Mario Ghossoub, 2016. "Optimal Insurance for a Minimal Expected Retention: The Case of an Ambiguity-Seeking Insurer," Risks, MDPI, vol. 4(1), pages 1-27, March.
    16. Ali al-Nowaihi & Sanjit Dhami & Mengxing Wei, 2018. "Quantum Decision Theory and the Ellsberg Paradox," CESifo Working Paper Series 7158, CESifo.
    17. Marcello Basili & Carlo Zappia, 2007. "The weight of argument and non-additive measures: a note," Department of Economic Policy, Finance and Development (DEPFID) University of Siena 003, Department of Economic Policy, Finance and Development (DEPFID), University of Siena.
    18. Ludwig, Alexander & Zimper, Alexander, 2006. "Investment behavior under ambiguity: The case of pessimistic decision makers," Mathematical Social Sciences, Elsevier, vol. 52(2), pages 111-130, September.
    19. Marcello Basili & Carlo Zappia, 2010. "Ambiguity and uncertainty in Ellsberg and Shackle," Cambridge Journal of Economics, Cambridge Political Economy Society, vol. 34(3), pages 449-474.
    20. Filiz-Ozbay, Emel & Gulen, Huseyin & Masatlioglu, Yusufcan & Ozbay, Erkut Y., 2022. "Comparing ambiguous urns with different sizes," Journal of Economic Theory, Elsevier, vol. 199(C).

    More about this item

    Keywords

    Ambiguity; Multiple priors; Unawareness;
    All these keywords.

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

    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:hal:journl:hal-03726359. 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: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    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.