Bray Theory Workshop

Abstract: I study a class of continuous-time games of learning and imperfect monitoring. A long-run player and a market share a common prior about the initial value of a Gaussian hidden state, and learn about it subsequent values by observing a noisy public signal. The long-run player can nevertheless control the evolution of this signal, and thus affect the market's belief. The public signal has an additive structure, and noise is Brownian. I derive conditions for a solution to an ordinary differential equation to characterize behavior in which the long-run player's equilibrium actions depends on the history of the game only through the market's correct belief. Using these conditions, I demonstrate the existence of equilibria in pure strategies for settings in which the long-run players's flow utility is nonlinear. The central finding is a learning-driven ratchet principle affecting incentives. I illustrate the economic implications of this principle in applications to monetary policy, earnings management, and career concerns.