Multi-Player Bayesian Learning with Misspecified Models

We consider strategic players who may have a misspecified view about an environment, and investigate their long-run behavior. Each period, players simultaneously take actions, observe a public outcome, and then update own belief about an uncertain economic state by using Bayes' rule. 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) actions. When a player has a biased view about the physical environment (e.g., overconfidence on own capability or prejudice on an opponent's capability), the presence of strategic interaction influences the size of the impact of misspecification, but not the direction. In particular, when the game is symmetric, the presence of strategic interaction amplifies the deviation of the long-run actions from those in the correctly specified model. When a player misspecifies the opponent's view about the environment (e.g., the player is not aware of the opponent's bias), the strategic interaction generates a directional impact for the long-run actions. We extensively discuss implications to a variety of applications, such as Cournot duopoly, team production, tournaments, and discrimination.