The Devil You Know: Rational Inattention to Discrete Choices when Prior Information Matters

In the seminal rational inattention model of Matĕjka and McKay (2015), logit demand arises from the discrete choice of agents who are uncertain about choice payoffs and who have access to a flexible, costly information acquisition technology (RI-logit). A notable limitation of this powerful framework is the lack of known general closed-form solutions, allowing the decision maker's prior information to differ across choices. In this paper, I solve the RI-logit model analytically for a large family of priors known as multivariate Tempered Stable (TS) distributions. In my analytical formulation, decision makers can be biased, display aversion to prior uncertainty, and thus tend to select choices that are familiar (i.e. for which they hold a less disperse prior). This result allows to study how the RI-logit choice probabilities react to an exogenous change in prior information, thus extending the model's applicability to a new range of settings where prior information matters. I provide one such application: I show how to use the closed-form RI-logit model to study the behavior of risk-averse investors who select risky projects in an environment characterized by epistemic uncertainty (risk-adjusted expected returns are unknown, but can be learnt at a cost.