A Multi-Agent Model of Misspecified Learning with Overconfidence

Abstract

Overconfidence has been extensively documented in psychology and economics. This paper studies the long-term interaction between two overconfident agents who learn about common payoff-relevant fundamentals, such as the quality of a joint project or their working environment, and choose how much effort to exert. Overconfidence causes agents to underestimate the fundamental 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: when one agent best responds to his own overconfidence, the other agent underestimates the fundamental more severely and takes a more extreme action, generating a positive feedback loop. The opposite pattern, mutually-limiting learning, arises when informational externalities are negative. Additionally, overconfidence can lead to Pareto improvement in welfare as it corrects the inefficiencies that arise in public good provision problems. This contrasts with the analogous single-agent environment, in which there is no scope for informational externalities, and overconfidence can only decrease welfare. Finally, we prove that under certain conditions, agents’ beliefs and effort choices converge to a steady state that is a Berk-Nash equilibrium.