We study learning and information acquisition by a Bayesian agent
whose prior belief is misspecified in the sense that it assigns probability
zero to the true state of the world. At each instant, the agent takes
an action and observes the corresponding payoff, which is the sum
of a fixed but unknown function of the action and an additive error
term. We provide a complete characterization of asymptotic actions
and beliefs when the agent's subjective state space is a doubleton.
A simple example with three actions shows that in a misspecified environment
a myopic agent's beliefs converge while a sufficiently patient agent's
beliefs do not. This illustrates a novel interaction between misspecification
and the agent's subjective discount rate.