We derive robust predictions in games involving flexible information acquisition, also known as rational inattention (Sims 2003). These predictions remain accurate regardless of the exact specification of players' learning abilities. Compared to scenarios where information is predetermined, rational inattention reduces welfare and introduces additional constraints on behavior. We show these constraints have an "all-or-nothing" flavor: the set of behaviors consistent with rational inattention is either dense or nowhere-dense in the set of behaviors consistent with exogenously given information. Moreover, the latter case is generic; the two knowledge regimes are behaviorally indistinguishable in most environments.

A seller offers a buyer a schedule of transfers and associated product qualities. After observing this schedule, the buyer chooses a flexible costly signal about his type. We show it is without loss to focus on a class of mechanisms that compensate the buyer for his learning costs. Focusing attention on these mechanisms allows one to employ techniques from both the information design and mechanism design toolkits.

We study a canonical flexible-learning model in which an agent chooses from a finite set of alternatives, the benefits from which depend on a stochastic state. Before making her decision, the agent chooses what signal to acquire about this state. Learning comes at a cost, which the agent subtracts from the expected benefit she derives from her final decision. After choosing her information, the agent observes a signal realization and takes an action.