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Maxmin Expected Utility with Non-Unique Prior

Author

Listed:
  • Itzhak Gilboa

    (Northwestern University [Evanston])

  • David Schmeidler

    (Tel Aviv University [Tel Aviv], OSU - Ohio State University [Columbus])

Abstract

Acts are functions from states of nature into finite-support distributions over a set of 'deterministic outcomes'. We characterize preference relations over acts which have a numerical representation by the functional J(f) = min > {∫ uo f dP / P∈C } where f is an act, u is a von Neumann-Morgenstern utility over outcomes, and C is a closed and convex set of finitely additive probability measures on the states of nature. In addition to the usual assumptions on the preference relation as transitivity, completeness, continuity and monotonicity, we assume uncertainty aversion and certainty-independence. The last condition is a new one and is a weakening of the classical independence axiom: It requires that an act f is preferred to an act g if and only if the mixture of f and any constant act h is preferred to the same mixture of g and h. If non-degeneracy of the preference relation is also assumed, the convex set of priors C is uniquely determined. Finally, a concept of independence in case of a non-unique prior is introduced.

Suggested Citation

  • Itzhak Gilboa & David Schmeidler, 1989. "Maxmin Expected Utility with Non-Unique Prior," Post-Print hal-00753237, HAL.
  • Handle: RePEc:hal:journl:hal-00753237
    DOI: 10.1016/0304-4068(89)90018-9
    Note: View the original document on HAL open archive server: https://hal-hec.archives-ouvertes.fr/hal-00753237
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    References listed on IDEAS

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    1. Daniel Ellsberg, 1961. "Risk, Ambiguity, and the Savage Axioms," The Quarterly Journal of Economics, Oxford University Press, vol. 75(4), pages 643-669.
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    Keywords

    Maxmin Expected Utility; Non-Unique Prior;

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