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Decision Making with Imprecise Probabilistic Information

  • Thibault Gajdos

    ()

    (CREST - Centre de Recherche en Économie et Statistique - INSEE - École Nationale de la Statistique et de l'Administration Économique, EUREQUA - Equipe Universitaire de Recherche en Economie Quantitative - UP1 - Université Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

  • Jean-Marc Tallon

    (EUREQUA - Equipe Universitaire de Recherche en Economie Quantitative - UP1 - Université Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

  • Jean-Christophe Vergnaud

    (EUREQUA - Equipe Universitaire de Recherche en Economie Quantitative - UP1 - Université Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

We develop an axiomatic approach to decision under uncertainty that explicitly takes into account the information available to the decision maker. The information is described by a set of priors and a reference prior. We define a notion of imprecision for this informational setting and show that a decision maker who is averse to information imprecision maximizes the minimum expected utility computed with respect to a subset of the set of initially given priors. The extent to which this set is reduced can be seen as a measure of imprecision aversion. This approach thus allows a lot of flexibility in modelling the decision maker attitude towards imprecision. In contrast, applyingGilboa-Schmeidler [1989] maxmin criterion to the initial set of priors amounts to assuming extreme pessimism.

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Paper provided by HAL in its series Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) with number halshs-00086021.

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Date of creation: 2004
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Publication status: Published in Journal of Mathematical Economics, Elsevier, 2004, 40 (6), pp.647-681. <10.1016/j.jmateco.2003.06.004>
Handle: RePEc:hal:cesptp:halshs-00086021
DOI: 10.1016/j.jmateco.2003.06.004
Note: View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-00086021
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