A Multi-Agent Model of Misspeciﬁed Learning with Overconﬁdence
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 over-conﬁdence, the other agent underestimates the fundamental more severely and takes an 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.