Higher-Order Misspecification and Equilibrium Stability

This paper considers a Bayesian learning problem where strategic players jointly learn an unknown economic state, and show that one's higher-order misspecification (i.e., one's misspecification about the opponent's misspecification) can have a significant impact on the equilibrium outcome. We consider a simple environmental problem where players' production, as well as an unknown state, affects the quality of the environment. Crucially, we assume that one of the players is unrealistically optimistic about the quality of the environment. When this optimism is common knowledge, the equilibrium outcome is continuous in the amount of optimism, and hence small optimism leads to approximately correct learning of the state. In contrast, when the optimism is not common knowledge and each player is unaware of the opponent having a different view about the world, the equilibrium outcome is discontinuous, and even vanishingly small optimism leads to completely incorrect learning. We then analyze a general Bayesian learning model and discuss when such discontinuity arises.