Dynamic Rationally Inattentive Discrete Choice: A Posterior-Based Approach

We adopt the posterior-based approach to study dynamic discrete choice problems with rational inattention. We show that the optimal solution for the Shannon entropy case is characterized by a system of equations that resembles the dynamic logit rule. We propose an efficient algorithm to solve this system and apply our model to explain phenomena such as status quo bias, confirmation bias, and belief polarization. We also study the dynamics of consideration sets. Unlike the choice-based approach, our approach applies to general uniformly posteriorseparable information cost functions. A key condition for our approach to work in dynamic models is the convexity of the difference between the discounted generalized entropy of the prior beliefs about the future states and the generalized entropy of the current posterior.