Rational Inattention to Discrete Choices with Stable Priors

How does prior information affect discrete choice? In the seminal rational inattention model of Matějka and McKay (2015), multinomial logit arises from the discrete choice of agents who are uncertain about choice payoffs and who have access to a flexible information acquisition technology (RI-logit). A key limitation of this powerful framework is the lack of known solutions that allow the decision maker's prior information to vary across choices: obtaining such solutions has remained an open problem in this literature. In this paper, I solve the RI-logit model analytically for two related families of priors known respectively as Positive Stable and Tempered Stable distributions. In my solution, the decision maker's prior information enters the choice probabilities through a choice-specific parameter, which can be read as shifting either the ex-ante expected utility of a risk-neutral decision maker, or the ex-ante riskiness perceived by a risk-averse one. These results complete the RI-logit framework by separating prior information from information that is endogenously acquired, and expand its empirical applications by making it possible to study how choice probabilities react to changes in prior information.