Modeling information acquisition via f-divergence and duality

We introduce a new cost function over experiments, f-information, based on the theory of multivariate statistical divergences, that generalizes Sims's classic model of rational inattention as well as the class of posterior-separable cost functions. We characterize its behavioral predictions by deriving optimality conditions that extend those of Matejka and McKay (2015) and Caplin, Dean, and Leahy (2019) beyond mutual information. Using these tools, we study the implications of f-information in a number of canonical decision problems. A strength of the framework is that it can be analyzed using familiar methods of microeconomics: convex duality and the Arrow-Pratt approach to expected utility.