Strategic information selection

Before choosing her action to match the state of the world, an agent observes a stream of messages generated by some unknown binary signal. The agent can either learn the underlying signal for free and update her belief accordingly or ignore the observed message and keep her prior belief. After each period the stream stops with positive probability and the final choice is made. We show that a Markovian agent with Gilboa-Schmeidler preferences learns and updates after confirming messages, but she ignores contradicting messages if her belief is sufficiently strong. Her threshold solely depends on the least precise signal. The agent has strictly higher anticipatory utility than an agent who uses every message to update. However, the latter has a higher chance to choose the correct outcome in the end. In a population of strategic agents, who only differ in their initial beliefs, polarization is inevitable.