IDEAS home Printed from https://ideas.repec.org/a/spr/joecth/v74y2022i2d10.1007_s00199-021-01408-y.html

Learning under unawareness

Author

Listed:
  • Simon Grant

    (Australian National University)

  • Idione Meneghel

    (Australian National University)

  • Rabee Tourky

    (Australian National University)

Abstract

We propose a model of learning when experimentation is possible, but unawareness and ambiguity matter. In this model, complete lack of information regarding the underlying data generating process is expressed as a (maximal) family of priors. These priors yield posterior inferences that become more precise as more information becomes available. As information accumulates, however, the individual’s level of awareness as encoded in the state space may expand. Such newly learned states are initially seen as ambiguous, but as evidence accumulates there is a gradual reduction of ambiguity.

Suggested Citation

  • 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.
  • Handle: RePEc:spr:joecth:v:74:y:2022:i:2:d:10.1007_s00199-021-01408-y
    DOI: 10.1007/s00199-021-01408-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00199-021-01408-y
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s00199-021-01408-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

    for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. Nehring, Klaus, 2009. "Imprecise probabilistic beliefs as a context for decision-making under ambiguity," Journal of Economic Theory, Elsevier, vol. 144(3), pages 1054-1091, May.
    3. Morris, Stephen, 1995. "The Common Prior Assumption in Economic Theory," Economics and Philosophy, Cambridge University Press, vol. 11(2), pages 227-253, October.
    4. Pivato, Marcus & Vergopoulos, Vassili, 2020. "Subjective expected utility with imperfect perception," Journal of Mathematical Economics, Elsevier, vol. 88(C), pages 104-122.
    5. repec:spo:wpmain:info:hdl:2441/eu4vqp9ompqllr09iepso50rh is not listed on IDEAS
    6. Igor Kopylov, 2016. "Subjective probability, confidence, and Bayesian updating," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 62(4), pages 635-658, October.
    7. Mongin Philippe, 1995. "Consistent Bayesian Aggregation," Journal of Economic Theory, Elsevier, vol. 66(2), pages 313-351, August.
    8. Kurz, Mordecai, 1994. "On the Structure and Diversity of Rational Beliefs," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(6), pages 877-900, October.
    9. Hervé Crès & Itzhak Gilboa & Nicolas Vieille, 2011. "Aggregation of multiple prior opinions," Post-Print hal-00656618, HAL.
    10. Larry G. Epstein & Martin Schneider, 2007. "Learning Under Ambiguity," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 74(4), pages 1275-1303.
    11. Kochov, Asen, 2018. "A behavioral definition of unforeseen contingencies," Journal of Economic Theory, Elsevier, vol. 175(C), pages 265-290.
    12. Hylland, Aanund & Zeckhauser, Richard J, 1979. "The Impossibility of Bayesian Group Decision Making with Separate Aggregation of Beliefs and Values," Econometrica, Econometric Society, vol. 47(6), pages 1321-1336, November.
    13. Dominiak, Adam & Tserenjigmid, Gerelt, 2022. "Ambiguity under growing awareness," Journal of Economic Theory, Elsevier, vol. 199(C).
    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. repec:spo:wpecon:info:hdl:2441/eu4vqp9ompqllr09iepso50rh is not listed on IDEAS
    16. Stephen G. Walker & Paul Damien & PuruShottam W. Laud & Adrian F. M. Smith, 1999. "Bayesian Nonparametric Inference for Random Distributions and Related Functions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(3), pages 485-527.
    17. Antoine Billot & Itzhak Gilboa & Dov Samet & David Schmeidler, 2012. "Probabilities as Similarity-Weighted Frequencies," World Scientific Book Chapters, in: Case-Based Predictions An Axiomatic Approach to Prediction, Classification and Statistical Learning, chapter 7, pages 169-184, World Scientific Publishing Co. Pte. Ltd..
    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. Crès, Hervé & Gilboa, Itzhak & Vieille, Nicolas, 2011. "Aggregation of multiple prior opinions," Journal of Economic Theory, Elsevier, vol. 146(6), pages 2563-2582.
    20. Massimo Marinacci, 2002. "Learning from ambiguous urns," Statistical Papers, Springer, vol. 43(1), pages 143-151, January.
    21. 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.
    22. Kalai, Ehud & Lehrer, Ehud, 1993. "Rational Learning Leads to Nash Equilibrium," Econometrica, Econometric Society, vol. 61(5), pages 1019-1045, September.
    23. 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.
    24. Itzhak Gilboa & Dov Samet & David Schmeidler, 2004. "Utilitarian Aggregation of Beliefs and Tastes," Journal of Political Economy, University of Chicago Press, vol. 112(4), pages 932-938, August.
    25. 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. Pei Kuang & Li Tang & Renbin Zhang & Tongbin Zhang, 2025. "Are survey stock price forecasts anchored by fundamental forecasts? A long-run perspective," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 79(2), pages 657-685, March.
    2. Chakravarty, Surajeet & Kelsey, David & Teitelbaum, Joshua C., 2022. "Reverse Bayesianism and act independence," Journal of Economic Theory, Elsevier, vol. 203(C).
    3. Rafael R. Guthmann, 2025. "Imperfect Competition as a Result of Unawareness," Review of Industrial Organization, Springer;The Industrial Organization Society, vol. 67(1), pages 35-53, June.
    4. Jianjun Miao, 2022. "Introduction to the special issue in honor of Larry Epstein," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 74(2), pages 329-333, September.
    5. Burkhard C. Schipper, 2024. "Predicting the Unpredictable under Subjective Expected Utility," Papers 2403.01421, arXiv.org, revised Feb 2025.

    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. Florian Mudekereza, 2025. "Robust Aggregation of Preferences," Papers 2504.07401, arXiv.org, revised Feb 2026.
    2. Eric Danan & Thibault Gajdos & Brian Hill & Jean-Marc Tallon, 2016. "Robust Social Decisions," American Economic Review, American Economic Association, vol. 106(9), pages 2407-2425, September.
    3. Hill , Brian & Danan , Eric, 2014. "Aggregating Tastes, Beliefs, and Attitudes Under Uncertainty," HEC Research Papers Series 1057, HEC Paris.
    4. repec:hal:pseose:halshs-01415412 is not listed on IDEAS
    5. Leo Kurata & Kensei Nakamura, 2025. "Reservation of Judgment and Robust Collective Decisions," Papers 2512.16240, arXiv.org.
    6. Bach Dong-Xuan, 2024. "Aggregation of misspecified experts," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 78(3), pages 923-943, November.
    7. Zuber, Stéphane, 2016. "Harsanyi’s theorem without the sure-thing principle: On the consistent aggregation of Monotonic Bernoullian and Archimedean preferences," Journal of Mathematical Economics, Elsevier, vol. 63(C), pages 78-83.
    8. Itzhak Gilboa, 2010. "Questions in Decision Theory," Annual Review of Economics, Annual Reviews, vol. 2(1), pages 1-19, September.
    9. Xiangyu Qu, 2017. "Separate aggregation of beliefs and values under ambiguity," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 63(2), pages 503-519, February.
    10. Thibault Gajdos & Jean-Christophe Vergnaud, 2013. "Decisions with conflicting and imprecise information," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(2), pages 427-452, July.
    11. McCarthy, David & Mikkola, Kalle & Thomas, Teruji, 2016. "Utilitarianism with and without expected utility," MPRA Paper 72578, University Library of Munich, Germany.
    12. Dominiak, Adam & Tserenjigmid, Gerelt, 2022. "Ambiguity under growing awareness," Journal of Economic Theory, Elsevier, vol. 199(C).
    13. Panagiotis Andrikopoulos & Nick Webber, 2019. "Understanding time-inconsistent heterogeneous preferences in economics and finance: a practice theory approach," Annals of Operations Research, Springer, vol. 282(1), pages 3-26, November.
    14. Fleurbaey, Marc & Zuber, Stéphane, 2017. "Fair management of social risk," Journal of Economic Theory, Elsevier, vol. 169(C), pages 666-706.
    15. Brian Hill, 2012. "Unanimity and the aggregation of multiple prior opinions," Working Papers hal-00712015, HAL.
    16. Wei Ma, 2025. "Discrete choice under risk and model uncertainty," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 65(2), pages 291-307, September.
    17. Stanca, Lorenzo, 2021. "Smooth aggregation of Bayesian experts," Journal of Economic Theory, Elsevier, vol. 196(C).
    18. Lasse Mononen, 2025. "Observable interpersonal utility comparisons," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 65(3), pages 629-644, November.
    19. ,, 2012. "The ex-ante aggregation of opinions under uncertainty," Theoretical Economics, Econometric Society, vol. 7(3), September.
    20. Mongin, Philippe & Pivato, Marcus, 2015. "Ranking multidimensional alternatives and uncertain prospects," Journal of Economic Theory, Elsevier, vol. 157(C), pages 146-171.
    21. McCarthy, David & Mikkola, Kalle & Thomas, Teruji, 2020. "Utilitarianism with and without expected utility," Journal of Mathematical Economics, Elsevier, vol. 87(C), pages 77-113.

    More about this item

    Keywords

    ;
    ;
    ;

    JEL classification:

    • 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:spr:joecth:v:74:y:2022:i:2:d:10.1007_s00199-021-01408-y. 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.