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Coping with Imprecise Information : A Decision Theoretic Approach

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  • Thibault Gadjos

    (Crest)

  • Jean-Marc Tallon

    (Crest)

  • Jean-Christophe Vergnaud

    (Crest)

Abstract

We provide a model of decision making under uncertainty in which the decision maker reacts toimprecision of the available data. Data is represented by a set of probability distributions. Weaxiomatize a decision criterion of the maxmin expected utility type, in which the revealed setof priors explicitly depends on the available data. We then characterize notions of comparativeaversion to imprecision of the data as well as traditional notions of risk aversion. Interestingly,the study of comparative aversion to imprecision can be done independently of the utilityfunction, which embeds risk attitudes. We also give a more specific result, in which the functionalrepresenting the decision maker’s preferences is the convex combination of the minimumexpected utility with respect to the available data and expected utility with respect to a subjectiveprobability distribution, interpreted as a reference prior. This particular form is shown tobe equivalent to some form of constant aversion to imprecision. We finally provide examples ofapplications first to unanimity rankings of imprecision and risk and then to optimal risk sharingarrangements.

Suggested Citation

  • Thibault Gadjos & Jean-Marc Tallon & Jean-Christophe Vergnaud, 2004. "Coping with Imprecise Information : A Decision Theoretic Approach," Working Papers 2004-14, Center for Research in Economics and Statistics.
  • Handle: RePEc:crs:wpaper:2004-14
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    References listed on IDEAS

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    1. Peter Klibanoff & Massimo Marinacci & Sujoy Mukerji, 2005. "A Smooth Model of Decision Making under Ambiguity," Econometrica, Econometric Society, vol. 73(6), pages 1849-1892, November.
    2. Gajdos, Thibault & Tallon, Jean-Marc & Vergnaud, Jean-Christophe, 2004. "Decision making with imprecise probabilistic information," Journal of Mathematical Economics, Elsevier, vol. 40(6), pages 647-681, September.
    3. Tapking, Jens, 2004. "Axioms for preferences revealing subjective uncertainty and uncertainty aversion," Journal of Mathematical Economics, Elsevier, vol. 40(7), pages 771-797, November.
    4. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    5. Sujoy Mukerji & Jean-Marc Tallon, 2001. "Ambiguity Aversion and Incompleteness of Financial Markets," Review of Economic Studies, Oxford University Press, vol. 68(4), pages 883-904.
    6. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
    7. Yaari, Menahem E., 1969. "Some remarks on measures of risk aversion and on their uses," Journal of Economic Theory, Elsevier, vol. 1(3), pages 315-329, October.
    8. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    9. Scarsini, Marco, 1992. "Dominance conditions in non-additive expected utility theory," Journal of Mathematical Economics, Elsevier, vol. 21(2), pages 173-184.
    10. Larry G. Epstein, 1999. "A Definition of Uncertainty Aversion," Review of Economic Studies, Oxford University Press, vol. 66(3), pages 579-608.
    11. Wojciech Olszewski, 2007. "Preferences Over Sets of Lotteries -super-1," Review of Economic Studies, Oxford University Press, vol. 74(2), pages 567-595.
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    Cited by:

    1. Thibault Gajdos & Feriel Kandil, 2008. "The ignorant observer," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 31(2), pages 193-232, August.
    2. Marciano Siniscalchi, 2009. "Vector Expected Utility and Attitudes Toward Variation," Econometrica, Econometric Society, vol. 77(3), pages 801-855, May.
    3. repec:hal:journl:halshs-00115722 is not listed on IDEAS
    4. Henry, Marc, 2007. "A representation of decision by analogy," Journal of Mathematical Economics, Elsevier, vol. 43(7-8), pages 771-794, September.

    More about this item

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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