On The Distributional Robustness Of Finite Rational Inattention Models

In this paper we study a Rational Inattention model in environments where the decision maker faces uncertainty about the true prior distribution over states. The decision maker seeks to select a stochastic choice rule over a finite set of alternatives that is robust to prior ambiguity. Following the robust stochastic optimization literature, we fully characterize the distributional robustness of the Rational Inattention model in terms of a tractable concave program. Exploiting this structure we establish necessary and sufficient conditions to construct robust consideration sets that account for the fact that the prior distribution is unknown. Finally, we quantify the impact of prior uncertainty, by introducing the notion of Worst-Case Sensitivity, which is de?ned as the worst-case rate of decrease in the expected utility of a robust decision maker when the degree of prior uncertainty vanishes. We show that this quantity is proportional to the standard deviation associated to the decision maker?s expected utility.