Characterizations of Smooth Ambiguity Based on Continuous and Discrete Data

Stefania Minardi · Andrei Savochkin

4 citations0/0 files storedMathematics of Operations Research

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Decision-Making and Behavioral Economics Game Theory and Applications Experimental Behavioral Economics Studies

Abstract

In the Anscombe-Aumann setup, we provide conditions for a collection of observations to be consistent with a well-known class of smooth ambiguity preferences (Klibanoff P, Marinacci M, Mukerji S (2005) A smooth model of decision making under ambiguity. Econometrica 73(6):1849–1892.). Each observation is assumed to take the form of an equivalence between an uncertain act and a certain outcome. We provide three results that describe these conditions for data sets of different cardinality. Our findings uncover surprising links between the smooth ambiguity model and classic mathematical results in complex and functional analysis.

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1961Risk, Ambiguity, and the Savage Axioms 1989Maxmin expected utility with non-unique prior 2005A Smooth Model of Decision Making under Ambiguity 2001Robust Control and Model Uncertainty 2006Ambiguity Aversion, Robustness, and the Variational Representation of Preferences 1967The Construction of Utility Functions from Expenditure Data 2012Ambiguity, Learning, and Asset Returns 2006Uncertainty Aversion with Second-Order Utilities and Probabilities

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