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The von Neumann/Morgenstern approach to ambiguity

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Author Info

  • Martin Dumav

    ()
    (Center for Mathematical Economics, Bielefeld University)

  • Maxwell B. Stinchcombe

    ()
    (Department of Economics, University of Texas, Austin)

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    Abstract

    A choice problem is risky (respectively ambiguous) if the decision maker is choosing between probability distributions (respectively sets of probability distributions) over utility relevant consequences. We provide an axiomatic foundation for and a representation of continuous linear preferences over sets of probabilities on consequences. The representation theory delivers: first and second order dominance for ambiguous problems; a utility interval based dominance relation that distinguishes between sources of uncertainty; a complete theory of updating convex sets of priors; a Bayesian theory of the value of ambiguous information structures; complete separations of attitudes toward risk and ambiguity; and new classes of preferences that allow decreasing relative ambiguity aversion and thereby rationalize recent challenges to many of the extant multiple prior models of ambiguity aversion. We also characterize a property of sets of priors, descriptive completeness, that resolves several open problems and allows multiple prior models to model as large a class of problems as the continuous linear preferences presented here.

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    File URL: http://www.imw.uni-bielefeld.de/n/upload/paper/577ef1154f3240ad5b9b413aa7346a1e.pdf
    File Function: First version, 2013
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    Bibliographic Info

    Paper provided by Bielefeld University, Center for Mathematical Economics in its series Working Papers with number 480.

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    Length: 38 pages
    Date of creation: May 2013
    Date of revision:
    Handle: RePEc:bie:wpaper:480

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    Web page: http://www.imw.uni-bielefeld.de/
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    Related research

    Keywords: Ambiguity; decision theory; multiple priors; descriptive completeness; continuous linear functionals on spaces of sets; constant and decreasing relative ambiguity aversion; zonoids;

    This paper has been announced in the following NEP Reports:

    References

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    1. Siniscalchi, Marciano, 2006. "A behavioral characterization of plausible priors," Journal of Economic Theory, Elsevier, vol. 128(1), pages 91-135, May.
    2. Athey, Susan, 2002. "Monotone Comparative Statics Under Uncertainty," Scholarly Articles 3372263, Harvard University Department of Economics.
    3. Simone Cerreia-Vioglio & Paolo Ghirardato & Fabio Maccheroni & Massimo Marinacci & Marciano Siniscalchi, 2010. "Rational Preferences under Ambiguity," Carlo Alberto Notebooks 169, Collegio Carlo Alberto.
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    14. Fang, Fang & Stinchcombe, Maxwell B. & Whinston, Andrew B., 2010. "Proper scoring rules with arbitrary value functions," Journal of Mathematical Economics, Elsevier, vol. 46(6), pages 1200-1210, November.
    15. Larry G. Epstein & Jiankang Zhang, 1999. "Subjective Probabilities on Subjectively Unambiguous Events," Carleton Economic Papers 99-18, Carleton University, Department of Economics.
    16. David S. Ahn, 2008. "Ambiguity Without a State Space," Review of Economic Studies, Oxford University Press, vol. 75(1), pages 3-28.
    17. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
    18. AMARANTE, Massimiliano, 2009. "Analogy in Decision-Making," Cahiers de recherche 14-2009, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    19. Stinchcombe, Maxwell B, 1997. "Countably Additive Subjective Probabilities," Review of Economic Studies, Wiley Blackwell, vol. 64(1), pages 125-46, January.
    20. Susan Athey, 2002. "Monotone Comparative Statics Under Uncertainty," The Quarterly Journal of Economics, MIT Press, vol. 117(1), pages 187-223, February.
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