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Model and Predictive Uncertainty: A Foundation for Smooth Ambiguity Preferences

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  • Tommaso Denti
  • Luciano Pomatto

Abstract

Smooth ambiguity preferences (Klibanoff, Marinacci, and Mukerji (2005)) describe a decision maker who evaluates each act f according to the twofold expectation V(f)=∫Pϕ(∫Ωu(f)dp)dμ(p) defined by a utility function u, an ambiguity index ϕ, and a belief μ over a set P of probabilities. We provide an axiomatic foundation for the representation, taking as a primitive a preference over Anscombe–Aumann acts. We study a special case where P is a subjective statistical model that is point identified, that is, the decision maker believes that the true law p∈P can be recovered empirically. Our main axiom is a joint weakening of Savage's sure‐thing principle and Anscombe–Aumann's mixture independence. In addition, we show that the parameters of the representation can be uniquely recovered from preferences, thereby making operational the separation between ambiguity attitude and perception, a hallmark feature of the smooth ambiguity representation.

Suggested Citation

  • Tommaso Denti & Luciano Pomatto, 2022. "Model and Predictive Uncertainty: A Foundation for Smooth Ambiguity Preferences," Econometrica, Econometric Society, vol. 90(2), pages 551-584, March.
    • Handle: RePEc:wly:emetrp:v:90:y:2022:i:2:p:551-584
    DOI: 10.3982/ECTA18009
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    References listed on IDEAS

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    2. Ozgur Evren, 2024. "Second-Order Representations: A Bayesian Approach," Working Papers w0291, New Economic School (NES).
    3. Michel Grabisch & Benjamin Monet & Vassili Vergopoulos, 2023. "Subjective expected utility through stochastic independence," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 76(3), pages 723-757, October.
    4. Toru Kitagawa & Sokbae Lee & Chen Qiu, 2022. "Treatment Choice with Nonlinear Regret," Papers 2205.08586, arXiv.org, revised Feb 2024.
    5. Borie, Dino, 2023. "Maxmin expected utility in Savage's framework," Journal of Economic Theory, Elsevier, vol. 210(C).
    6. Yoram Halevy & David Walker-Jones & Lanny Zrill, 2023. "Difficult Decisions," Working Papers tecipa-753, University of Toronto, Department of Economics.

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