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The von Neumann/Morgenstern approach to ambiguity

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  • 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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    Related research

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

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    2. Siniscalchi, Marciano, 2006. "A behavioral characterization of plausible priors," Journal of Economic Theory, Elsevier, vol. 128(1), pages 91-135, May.
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    4. Susan Athey, 2002. "Monotone Comparative Statics Under Uncertainty," The Quarterly Journal of Economics, MIT Press, vol. 117(1), pages 187-223, February.
    5. 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.
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    8. Maxwell B. Stinchcombe, 1994. "Countably Additive Subjective Probabilities," CARE Working Papers 9403, The University of Texas at Austin, Center for Applied Research in Economics.
    9. Wakker, Peter P, 2001. "Testing and Characterizing Properties of Nonadditive Measures through Violations of the Sure-Thing Principle," Econometrica, Econometric Society, vol. 69(4), pages 1039-59, July.
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    18. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
    19. Athey, Susan, 2002. "Monotone Comparative Statics Under Uncertainty," Scholarly Articles 3372263, Harvard University Department of Economics.
    20. David Schmeidler, 1989. "Subjective Probability and Expected Utility without Additivity," Levine's Working Paper Archive 7662, David K. Levine.
    21. Emir Kamenica & Matthew Gentzkow, 2011. "Bayesian Persuasion," American Economic Review, American Economic Association, vol. 101(6), pages 2590-2615, October.
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