Ambiguity from the Differential Viewpoint

Abstract

The objective of this paper is to show how ambiguity, and a decision maker (DM)'s response to it, can be modeled formally in the context of a very general decision model. In the first part of the paper we introduce an "unambiguous preference" relation derived from the DM's preferences, and show that it can be represented by a set of probability measures. We provide such set with a simple differential interpretation and argue that it represents the DM's perception of the "ambiguity" present in the decision problem. Given the notion of ambiguity, we show that preferences can be represented so as to provide an intuitive representation of ambiguity attitudes. In the second part of the paper we provide some extensions and "applications" of these ideas. We present an axiomatic characterization of the α-MEU decision rule. We also consider a simple dynamic choice setting and show the characterization of the updating rule that revises every prior in the aforementioned set by Bayes's rule; i.e., the generalized Bayesian updating rule.

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