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Eliciting Second-Order Beliefs

Author

Listed:
  • Subir Bose

    (University of Leicester)

  • Arup Daripa

    (Birkbeck, University of London)

Abstract
We study elicitation of subjective beliefs of an agent facing ambiguity (model uncertainty): the agent has a non-singleton set of (first-order) priors on an event and a second-order prior on these first-order belief-states. Such a two-stage decomposition of uncertainty and non-reduction of compound lotteries resulting from nonneutrality to the second-order distribution plays an important role in resolving the Ellsberg Paradox. The problem of eliciting beliefs on unobservable belief-states with ambiguity-sensitive agents is novel, and we introduce new elicitation techniques using report-dependent prize variations. We construct a direct revelation mechanism that induces truthful reporting of the first-order belief states as well as the secondorder distribution on the belief-states as the unique best response. The technique requires knowledge of the sensitivity function to second-order distribution (capturing ambiguity attitude) and the vN-M utility function, which we also elicit.

Suggested Citation

  • Subir Bose & Arup Daripa, 2017. "Eliciting Second-Order Beliefs," Birkbeck Working Papers in Economics and Finance 1710, Birkbeck, Department of Economics, Mathematics & Statistics.
  • Handle: RePEc:bbk:bbkefp:1710
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    File URL: https://eprints.bbk.ac.uk/id/eprint/29819
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    References listed on IDEAS

    as
    1. Segal, Uzi, 1990. "Two-Stage Lotteries without the Reduction Axiom," Econometrica, Econometric Society, vol. 58(2), pages 349-377, March.
    2. Segal, Uzi, 1987. "The Ellsberg Paradox and Risk Aversion: An Anticipated Utility Approach," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 28(1), pages 175-202, February.
    3. Bose, Subir & Daripa, Arup, 2022. "Eliciting ambiguous beliefs using constructed ambiguous acts: Alpha-maxmin," Journal of Mathematical Economics, Elsevier, vol. 103(C).
    4. Andrew Schotter & Isabel Trevino, 2014. "Belief Elicitation in the Laboratory," Annual Review of Economics, Annual Reviews, vol. 6(1), pages 103-128, August.
    5. Edi Karni, 2018. "A Mechanism for Eliciting Second-Order Beliefs and the Inclination to Choose," American Economic Journal: Microeconomics, American Economic Association, vol. 10(2), pages 275-285, May.
    6. Edi Karni, 2009. "A Mechanism for Eliciting Probabilities," Econometrica, Econometric Society, vol. 77(2), pages 603-606, March.
    7. Peter Wakker & Daniel Deneffe, 1996. "Eliciting von Neumann-Morgenstern Utilities When Probabilities Are Distorted or Unknown," Management Science, INFORMS, vol. 42(8), pages 1131-1150, August.
    8. Chambers, Christopher P., 2008. "Proper scoring rules for general decision models," Games and Economic Behavior, Elsevier, vol. 63(1), pages 32-40, May.
    9. Robert F. Nau, 2006. "Uncertainty Aversion with Second-Order Utilities and Probabilities," Management Science, INFORMS, vol. 52(1), pages 136-145, January.
    10. Christopher P. Chambers & Nicolas S. Lambert, 2021. "Dynamic Belief Elicitation," Econometrica, Econometric Society, vol. 89(1), pages 375-414, January.
    11. Loïc Berger & Massimo Marinacci, 2020. "Model Uncertainty in Climate Change Economics: A Review and Proposed Framework for Future Research," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 77(3), pages 475-501, November.
    12. Loïc Berger & Nicolas Berger & Valentina Bosetti & Itzhak Gilboa & Lars Peter Hansen & Christopher Jarvis & Massimo Marinacci & Richard D. Smith, 2020. "Uncertainty and decision-making during a crisis: How to make policy decisions in the COVID-19 context?," Working Papers 666, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    13. Kyoungwon Seo, 2009. "Ambiguity and Second-Order Belief," Econometrica, Econometric Society, vol. 77(5), pages 1575-1605, September.
    14. 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.
    15. Manski, Charles F. & Neri, Claudia, 2013. "First- and second-order subjective expectations in strategic decision-making: Experimental evidence," Games and Economic Behavior, Elsevier, vol. 81(C), pages 232-254.
    16. 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.
    17. Subir Bose & Arup Daripa, 2016. "Eliciting Ambiguous Beliefs Under alpha-Maxmin Preference," Birkbeck Working Papers in Economics and Finance 1601, Birkbeck, Department of Economics, Mathematics & Statistics.
    18. Karl Schlag & James Tremewan & Joël Weele, 2015. "A penny for your thoughts: a survey of methods for eliciting beliefs," Experimental Economics, Springer;Economic Science Association, vol. 18(3), pages 457-490, September.
    19. Gneiting, Tilmann & Raftery, Adrian E., 2007. "Strictly Proper Scoring Rules, Prediction, and Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 359-378, March.
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    More about this item

    Keywords

    Ambiguity; second-order beliefs; elicitation of second-order beliefs (support and distribution); Klibanoff-Marinacci-Mukerji (2005) representation; elicitation of second-order-distribution-sensitivity function; elicitation of the vN-M utility function.;
    All these keywords.

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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