A multi-agent model of misspecified learning with overconfidence

This paper studies the long-term interaction between two overconfident agents who choose how much effort to exert while learning about their environment. Overconfidence causes agents to underestimate either a common fundamental, such as the underlying quality of their project, or their counterpart's ability, to justify their worse-than-expected performance. We show that in many settings, agents create informational externalities for each other. When informational externalities are positive, the agents' learning processes are mutually-reinforcing: one agent best responding to his own overconfidence causes the other agent to reach a more distorted belief and take more extreme actions, generating a positive feedback loop. The opposite pattern, mutually-limiting learning, arises when informational externalities are negative. We also show that in our multi-agent environment, overconfidence can lead to Pareto improvement in welfare. Finally, we prove that under certain conditions, agents' beliefs and effort choices converge to a steady state that is a Berk-Nash equilibrium.