# The Mathematics of Bayesian Learning Traps

A Bayesian decision maker does not know which of several parameters is true. In each period she chooses an action **a** from an open subset of **R ^{n}**, observes an outcome, and updates her beliefs. There is an action

**a***that is uninformative in the sense that when it is chosen all parameters give the same distribution over outcomes, and consequently beliefs do not change. We give conditions under which a policy specifying an action as a function of the current belief can result in a positive probability that the sequence of beliefs converge to a belief at which

**a***is chosen, so that learning is asymptotically incomplete. Such a policy can be optimal even when the decision maker is not myopic and values experimentation.