Misspecified Bayesian Learning by Strategic Players: First-Order Misspecification and Higher-Order Misspecification

We consider strategic players who may have a misspecified view about the world, and investigate their long-run behavior when they learn an unknown state from public signals over time. Our framework is flexible and allows for higher-order misspecification, in that a player may have a bias about the physical environment, a bias about the opponent's bias about the physical environment, and so on. We provide a condition under which players' beliefs and actions converge to a steady state, and then characterize how one's misspecification influences the long-run (steady-state) outcome. We apply these results to various economic examples such as Cournot competition, team production, and discrimination. We find that higher-order misspecification can have a significant impact on the equilibrium outcome: One's overconfidence can have opposite effects on the equilibrium outcome, depending on whether the opponent is aware of this bias or not.