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A subjective theory of compound lotteries

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  • Haluk Ergin
  • Faruk Gul

Abstract

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

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Bibliographic Info

Paper provided by Econometric Society in its series Econometric Society 2004 North American Summer Meetings with number 152.

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Date of creation: 11 Aug 2004
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Handle: RePEc:ecm:nasm04:152

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

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References

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  1. Ghirardato, Paolo & Marinacci, Massimo, 2002. "Ambiguity Made Precise: A Comparative Foundation," Journal of Economic Theory, Elsevier, vol. 102(2), pages 251-289, February.
  2. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
  3. Epstein, Larry G & Zhang, Jiankang, 2001. "Subjective Probabilities on Subjectively Unambiguous Events," Econometrica, Econometric Society, vol. 69(2), pages 265-306, March.
  4. Gilboa, Itzhak, 1987. "Expected utility with purely subjective non-additive probabilities," Journal of Mathematical Economics, Elsevier, vol. 16(1), pages 65-88, February.
  5. 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.
  6. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
  7. Sujoy Mukerji & Peter Klibanoff, 2002. "A Smooth Model of Decision,Making Under Ambiguity," Economics Series Working Papers 113, University of Oxford, Department of Economics.
  8. Kreps, David M & Porteus, Evan L, 1978. "Temporal Resolution of Uncertainty and Dynamic Choice Theory," Econometrica, Econometric Society, vol. 46(1), pages 185-200, January.
  9. David Schmeidler, 1989. "Subjective Probability and Expected Utility without Additivity," Levine's Working Paper Archive 7662, David K. Levine.
  10. Epstein, L.G. & Zhang, J., 1998. "Subjective Probabilities on Subjectivity Unambiguous Event," RCER Working Papers 456, University of Rochester - Center for Economic Research (RCER).
  11. Machina,Mark & Schmeidler,David, 1991. "A more robust definition of subjective probability," Discussion Paper Serie A 365, University of Bonn, Germany.
  12. Gul, Faruk, 1991. "A Theory of Disappointment Aversion," Econometrica, Econometric Society, vol. 59(3), pages 667-86, May.
  13. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
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Cited by:
  1. Gino Cateau, 2006. "Guarding Against Large Policy Errors under Model Uncertainty," Working Papers 06-13, Bank of Canada.
  2. 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.
  3. Massimo Guidolin & Francesca Rinaldi, 2010. "Ambiguity in asset pricing and portfolio choice: a review of the literature," Working Papers 2010-028, Federal Reserve Bank of St. Louis.
  4. Peter Klibanoff & Massimo Marinacci & Sujoy Mukerji, 2006. "Recursive Smooth Ambiguity Preferences," Carlo Alberto Notebooks 17, Collegio Carlo Alberto, revised 2008.
  5. Klaus Nehring, 2006. "Decision-Making in the Context of Imprecise Probabilistic Beliefs," Economics Working Papers 0034, Institute for Advanced Study, School of Social Science.
  6. repec:clg:wpaper:2013-27 is not listed on IDEAS
  7. Simon Grant & Atsushi Kajii, 2005. "Probabilistically Sophisticated Multiple Priors," KIER Working Papers 608, Kyoto University, Institute of Economic Research.
  8. Gino Cateau, 2005. "Monetary Policy under Model and Data-Parameter Uncertainty," Working Papers 05-6, Bank of Canada.
  9. Cateau, Gino, 2007. "Monetary policy under model and data-parameter uncertainty," Journal of Monetary Economics, Elsevier, vol. 54(7), pages 2083-2101, October.

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