Dynamic consistency and rectangularity for the smooth ambiguity model

We study the Smooth Ambiguity decision criterion in the dynamic setting to understand when it can satisfy the Dynamic Consistency and Consequentialism properties. These properties allow one to rewrite the decision criterion recursively and solve for optimal decisions by Dynamic Programming. Our result characterizes the possibility of having these properties through a condition that resembles Epstein and Schneider's (2003) rectangularity condition for the maxmin model. At the same time, we show that Dynamic Consistency and Consequentialism can be achieved for Smooth Ambiguity preferences in a narrower set of scenarios than one would hope for.