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A subjective theory of compound lotteries


  • Haluk Ergin
  • Faruk Gul


We develop a Savage-type model of choice under uncertainty in which agents identify uncertain prospects with subjective compound lotteries. Our theory permits issue preference; that is, agents may not be indifferent among gambles that yield the same probability distribution if they depend on different issues. Hence, we establish subjective foundations for the Anscombe-Aumann framework and other models with two different types of probabilities. We define second-order risk as risk that resolves in the first stage of the compound lottery and show the equivalence of aversion to this risk with issue preference, the Ellsberg paradox, and uncertainty aversion

Suggested Citation

  • Haluk Ergin & Faruk Gul, 2004. "A subjective theory of compound lotteries," Econometric Society 2004 North American Summer Meetings 152, Econometric Society.
  • Handle: RePEc:ecm:nasm04:152

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    References listed on IDEAS

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    1. repec:clg:wpaper:2013-27 is not listed on IDEAS
    2. Klibanoff, Peter & Marinacci, Massimo & Mukerji, Sujoy, 2009. "Recursive smooth ambiguity preferences," Journal of Economic Theory, Elsevier, vol. 144(3), pages 930-976, May.
    3. Gino Cateau, 2005. "Monetary Policy under Model and Data-Parameter Uncertainty," Staff Working Papers 05-6, Bank of Canada.
    4. Massimo Guidolin & Francesca Rinaldi, 2013. "Ambiguity in asset pricing and portfolio choice: a review of the literature," Theory and Decision, Springer, vol. 74(2), pages 183-217, February.
    5. Cateau, Gino, 2007. "Monetary policy under model and data-parameter uncertainty," Journal of Monetary Economics, Elsevier, vol. 54(7), pages 2083-2101, October.
    6. Hansen, Lars Peter & Sargent, Thomas J., 2007. "Recursive robust estimation and control without commitment," Journal of Economic Theory, Elsevier, vol. 136(1), pages 1-27, September.
    7. Robert F. Nau, 2006. "Uncertainty Aversion with Second-Order Utilities and Probabilities," Management Science, INFORMS, vol. 52(1), pages 136-145, January.
    8. Chew, Soo Hong & Sagi, Jacob S., 2008. "Small worlds: Modeling attitudes toward sources of uncertainty," Journal of Economic Theory, Elsevier, vol. 139(1), pages 1-24, March.
    9. Zvi Safra & Uzi Segal, 2005. "Are Universal Preferences Possible? Calibration Results for Non-Expected Utility Theories," Boston College Working Papers in Economics 633, Boston College Department of Economics.
    10. Philipp Karl ILLEDITSCH, 2009. "Ambiguous Information, Risk Aversion, and Asset Pricing," 2009 Meeting Papers 802, Society for Economic Dynamics.
    11. Simon Grant & Atsushi Kajii, 2005. "Probabilistically Sophisticated Multiple Priors," KIER Working Papers 608, Kyoto University, Institute of Economic Research.
    12. Gino Cateau, 2006. "Guarding Against Large Policy Errors under Model Uncertainty," Staff Working Papers 06-13, Bank of Canada.
    13. 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.
    14. Klaus Nehring, 2006. "Decision-Making in the Context of Imprecise Probabilistic Beliefs," Economics Working Papers 0034, Institute for Advanced Study, School of Social Science.

    More about this item


    issue preference; uncertainty aversion; Ellsberg paradox; Savage; compound lotteries;

    JEL classification:

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

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