Abstract

A decision problem under uncertainty is often given with a piece of objective but imprecise information about the states of the world such as in the Ellsberg urn. By incorporating such information into the smooth ambiguity model of Seo (2009), we characterize a class of smooth ambiguity representations whose second-order beliefs are consistent with the objective information. As a corollary, we provide an axiomatization for the second-order expected utility, which has been studied by Nau (2001), Neilson (2009), Grant, Polak, and Strzalecki (2009), Strzalecki (2011), and Ghirardato and Pennesi (2019). In our model, attitude toward uncertainty can be disentangled from a perception about uncertainty and connected with attitude toward reduction of compound lotteries.

 

Introduction

Choice under uncertainty is an important aspect of decision making. Since Ellsberg’s seminal work, it is admitted that a decision maker’s behavior may be inconsistent with a probabilistic belief (or a subjective probability measure) about the states of the world. Such a situation is called ambiguity and has been studied by several models of decision making, such as the Choquet expected utility (Schmeidler [31]), the maxmin expected utility (Gilboa and Schmeidler [12]), and the smooth ambiguity model (Klibanoff, Marinacci, and Mukerji [22] and Seo [33]).

 

WP037

2021.12

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