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Second order beliefs models of choice under imprecise risk: non-additive second order beliefs vs. nonlinear second order utility

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  • Giraud, Raphaël

    ()
    (Department of Economics, University of Paris 8, LED)

Abstract

This paper discusses models of choice under imprecise objective probabilistic information featuring beliefs about beliefs -- second order beliefs. A new model, called Second Order Dual Expected Utility (SODEU) featuring non-additive second order beliefs is introduced, axiomatized and systematically contrasted with the leading alternative model of this kind, the Second Order Subjective Expected Utility (SOSEU) model (Klibanoff, Marinacci, Mukerji, 2005; Nau, 2006; Seo, 2009) for which, for the sake of comparison, we provide a new axiomatization, dispensing with the complex constructs used in extant axiomatizations. Ambiguity attitude and attitude toward information in general are discussed and characterized.

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Article provided by Econometric Society in its journal Theoretical Economics.

Volume (Year): (Forthcoming)
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Handle: RePEc:the:publsh:569

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Keywords: Imprecise probabilistic information; second order beliefs; non-additive probabilities; ambiguity aversion; Ellsberg paradox; Choquet integral;

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  1. Larry G. Epstein, 2010. "A Paradox for the “Smooth Ambiguity” Model of Preference," Econometrica, Econometric Society, Econometric Society, vol. 78(6), pages 2085-2099, November.
  2. Thibault Gajdos & Jean-Marc Tallon & Jean-Christophe Vergnaud, 2002. "Decision Making with Imprecise Probabilistic Information," ICER Working Papers - Applied Mathematics Series, ICER - International Centre for Economic Research 18-2003, ICER - International Centre for Economic Research, revised May 2003.
  3. Gollier, Christian, 2009. "Portfolio Choices and Asset Prices: The Comparative Statics of Ambiguity Aversion," TSE Working Papers 09-068, Toulouse School of Economics (TSE).
  4. Peter Klibanoff & Massimo Marinacci & Sujoy Mukerji, 2002. "A smooth model of decision making under ambiguity," ICER Working Papers - Applied Mathematics Series, ICER - International Centre for Economic Research 11-2003, ICER - International Centre for Economic Research, revised Apr 2003.
  5. Peter Klibanoff & Massimo Marinacci & Sujoy Mukerji, 2011. "On the Smooth Ambiguity Model: A Reply," Working Papers 410, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
  6. Raphaël Giraud & Jean-Marc Tallon, 2011. "Are beliefs a matter of taste? A case for Objective Imprecise Information," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00502781, HAL.
  7. Simone Cerreia-Vioglio & Fabio Maccheroni & Massimo Marinacci & Luigi Montrucchio, 2010. "Singed Integral Representations of Comonotonic Additive Functionals," Working Papers 366, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
  8. Gajdos, T. & Hayashi, T. & Tallon, J.-M. & Vergnaud, J.-C., 2008. "Attitude toward imprecise information," Journal of Economic Theory, Elsevier, vol. 140(1), pages 27-65, May.
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  10. Massimo Marinacci & Paolo Ghirardato, 2001. "Risk, ambiguity, and the separation of utility and beliefs," ICER Working Papers - Applied Mathematics Series, ICER - International Centre for Economic Research 21-2001, ICER - International Centre for Economic Research.
  11. David Ahn & Syngjoo Choi & Douglas Gale & Shachar Kariv, 2008. "Estimating Ambiguity Aversion in a Portfolio Choice Experiment," Levine's Working Paper Archive 122247000000001989, David K. Levine.
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  13. Leandro Nascimento & Gil Riella, 2013. "Second-order ambiguous beliefs," Economic Theory, Springer, vol. 52(3), pages 1005-1037, April.
  14. Amarante, Massimiliano, 2009. "Foundations of neo-Bayesian statistics," Journal of Economic Theory, Elsevier, vol. 144(5), pages 2146-2173, September.
  15. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, Econometric Society, vol. 55(1), pages 95-115, January.
  16. David S. Ahn, 2008. "Ambiguity Without a State Space," Review of Economic Studies, Oxford University Press, vol. 75(1), pages 3-28.
  17. 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.
  18. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
  19. Kyoungwon Seo, 2009. "Ambiguity and Second-Order Belief," Econometrica, Econometric Society, Econometric Society, vol. 77(5), pages 1575-1605, 09.
  20. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, Econometric Society, vol. 57(3), pages 571-87, May.
  21. Zhou, Lin, 1999. "Subjective probability theory with continuous acts," Journal of Mathematical Economics, Elsevier, vol. 32(1), pages 121-130, August.
  22. repec:hal:journl:halshs-00451982 is not listed on IDEAS
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