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Unambiguous Events and Dynamic Choquet Preferences

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  • Dominiak, Adam
  • Lefort, Jean-Philippe

Abstract

This paper explores the relationship between dynamic consistency and the existing notions of unambiguous events for Choquet expected utility preferences. A decision maker is faced with an information structure represented by a filtration. We show that the decision maker's preferences respect dynamic consistency on a fixed filtration if and only if the last stage of the filtration is composed of unambiguous events in the sense of Nehring (1999). Adopting two axioms, conditional certainty equivalence consistency and constrained dynamic consistency to filtration measurable acts, it is shown that the decision maker respects these two axioms on a fixed filtration if and only if the last stage of the filtration is made up of unambiguous events the sense of Zhang (2002).

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Paper provided by University of Heidelberg, Department of Economics in its series Working Papers with number 0489.

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Date of creation: 21 Sep 2009
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Handle: RePEc:awi:wpaper:0489

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Keywords: Choquet expected utility; unambiguous events; filtration; updating; dynamic consistency; consequentialism;

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References

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  1. Klaus Nehring & Michael Magill & Julian R. Betts, 2003. "Capacities And Probabilistic Beliefs: A Precarious Coexistence," Working Papers 978, University of California, Davis, Department of Economics.
  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. Kopylov, Igor, 2007. "Subjective probabilities on "small" domains," Journal of Economic Theory, Elsevier, vol. 133(1), pages 236-265, March.
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  6. Paolo Ghirardato, 2002. "Revisiting Savage in a conditional world," Economic Theory, Springer, vol. 20(1), pages 83-92.
  7. Lefort, Jean-Philippe & Dominiak, Adam & Dürsch, Peter, 2012. "A Dynamic Ellsberg Urn Experiment," Economics Papers from University Paris Dauphine 123456789/7357, Paris Dauphine University.
  8. Machina, Mark J, 1989. "Dynamic Consistency and Non-expected Utility Models of Choice under Uncertainty," Journal of Economic Literature, American Economic Association, vol. 27(4), pages 1622-68, December.
  9. Jurgen Eichberger & Simon Grant & David Kelsey, 2006. "Updating Choquet Beliefs," Discussion Papers 0607, Exeter University, Department of Economics.
  10. Ghirardato, Paolo & Maccheroni, Fabio & Marinacci, Massimo, 2004. "Differentiating ambiguity and ambiguity attitude," Journal of Economic Theory, Elsevier, vol. 118(2), pages 133-173, October.
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  12. Jiankang Zhang, 1999. "Subjective Ambiguity, Expected Utility and Choquet Expected Utility," Carleton Economic Papers 99-19, Carleton University, Department of Economics, revised Aug 2002.
  13. Sarin, Rakesh K & Wakker, Peter, 1992. "A Simple Axiomatization of Nonadditive Expected Utility," Econometrica, Econometric Society, vol. 60(6), pages 1255-72, November.
  14. Grant, Simon & Eichberger, Jürgen & Kelsey, David, 2004. "CEU Preferences and Dynamic Consistency," Sonderforschungsbereich 504 Publications 04-47, Sonderforschungsbereich 504, Universität Mannheim & Sonderforschungsbereich 504, University of Mannheim.
  15. Paolo Ghirardato & Fabio Maccheroni & Massimo Marinacci, 2007. "Revealed Ambiguity and Its Consequences: Updating," Carlo Alberto Notebooks 44, Collegio Carlo Alberto.
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  20. Wakker, Peter, 1989. "Continuous subjective expected utility with non-additive probabilities," Journal of Mathematical Economics, Elsevier, vol. 18(1), pages 1-27, February.
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  23. Eichberger, Jürgen & Grant, Simon & Lefort, Jean-Philippe, 2008. "Neo-additive capacities and updating," Sonderforschungsbereich 504 Publications 08-31, Sonderforschungsbereich 504, Universität Mannheim & Sonderforschungsbereich 504, University of Mannheim.
  24. Gilboa, Itzhak, 1987. "Expected utility with purely subjective non-additive probabilities," Journal of Mathematical Economics, Elsevier, vol. 16(1), pages 65-88, February.
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Citations

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Cited by:
  1. André Lapied & Pascal Toquebeuf, 2009. "Consistent dynamic choice and non-expected utility preferences," Working Papers hal-00416214, HAL.
  2. Lapied, André & Toquebeuf, Pascal, 2012. "Dynamically consistent CEU preferences on f-convex events," Mathematical Social Sciences, Elsevier, vol. 63(3), pages 252-256.
  3. Jürgen Eichberger & Simon Grant & David Kelsey, 2012. "When is Ambiguity-Attitude Constant?," CESifo Working Paper Series 3768, CESifo Group Munich.
  4. Andre Lapied & Pascal Toquebeuf, 2012. "Dynamically consistent CEU preferences," TEPP Working Paper 2012-10, TEPP.
  5. Dominiak, Adam, 2013. "Iterated Choquet expectations: A possibility result," Economics Letters, Elsevier, vol. 120(2), pages 155-159.

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