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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 UCLA Department of Economics in its series Levine's Bibliography with number 506439000000000406.

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Date of creation: 14 Mar 2003
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Handle: RePEc:cla:levrem:506439000000000406

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  1. Gilboa, Itzhak, 1987. "Expected utility with purely subjective non-additive probabilities," Journal of Mathematical Economics, Elsevier, vol. 16(1), pages 65-88, February.
  2. Mark J. Machina & David Schmeidler, 1990. "A More Robust Definition of Subjective Probability," Discussion Paper Serie A 306, University of Bonn, Germany.
  3. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-87, May.
  4. Peter Klibanoff & Massimo Marinacci & Sujoy Mukerji, 2002. "A smooth model of decision making under ambiguity," ICER Working Papers - Applied Mathematics Series 11-2003, ICER - International Centre for Economic Research, revised Apr 2003.
  5. Epstein, L.G. & Zhang, J., 1998. "Subjective Probabilities on Subjectivity Unambiguous Event," RCER Working Papers 456, University of Rochester - Center for Economic Research (RCER).
  6. Uzi Segal, 1985. "The Ellsberg Paradox and Risk Aversion: An Anticipated Utility Approach," UCLA Economics Working Papers 362, UCLA Department of Economics.
  7. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
  8. Ghirardato, Paolo & Marinacci, Massimo, 2002. "Ambiguity Made Precise: A Comparative Foundation," Journal of Economic Theory, Elsevier, vol. 102(2), pages 251-289, February.
  9. Larry G. Epstein & Jiankang Zhang, 1999. "Subjective Probabilities on Subjectively Unambiguous Events," Carleton Economic Papers 99-18, Carleton University, Department of Economics.
  10. David M Kreps & Evan L Porteus, 1978. "Temporal Resolution of Uncertainty and Dynamic Choice Theory," Levine's Working Paper Archive 625018000000000009, David K. Levine.
  11. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
  12. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
  13. Gul, Faruk, 1991. "A Theory of Disappointment Aversion," Econometrica, Econometric Society, vol. 59(3), pages 667-86, May.
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Cited by:
  1. Simon Grant & Atsushi Kajii, 2005. "Probabilistically Sophisticated Multiple Priors," KIER Working Papers 608, Kyoto University, Institute of Economic Research.
  2. Gino Cateau, 2005. "Monetary Policy under Model and Data-Parameter Uncertainty," Working Papers 05-6, Bank of Canada.
  3. David Cooper & David Johnson, 2013. "Ambiguity in Performance Pay: An Online Experiment," Working Papers 2013-27, Department of Economics, University of Calgary, revised 14 Nov 2013.
  4. Gino Cateau, 2006. "Guarding Against Large Policy Errors under Model Uncertainty," Working Papers 06-13, Bank of Canada.
  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. Cateau, Gino, 2007. "Monetary policy under model and data-parameter uncertainty," Journal of Monetary Economics, Elsevier, vol. 54(7), pages 2083-2101, October.
  7. 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.
  8. Klibanoff, Peter & Marinacci, Massimo & Mukerji, Sujoy, 2009. "Recursive smooth ambiguity preferences," Journal of Economic Theory, Elsevier, vol. 144(3), pages 930-976, May.

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