Randomization and Ambiguity Aversion

Abstract

We propose a model of preferences in which the effect of randomization on ambiguity depends on how the unknown probability law is determined. We adopt the framework of Anscombe and Aumann (1963) and relax the axioms. In the resulting representation of the individual's preference, the individual has a collection of sets of priors <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi mathvariant="script">M</a:mi> </a:math>. She believes that before she moves, nature has chosen an unknown scenario (a set of priors) from <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"> <d:mi mathvariant="script">M</d:mi> </d:math>, and from that scenario, nature will choose a prior after she moves. The representation illustrates how randomization may partially eliminate the effect of ambiguity.