Two-Sided Learning and the Ratchet Principle

Abstract

I study a class of continuous-time games of learning and imperfect monitoring. A longrun player and a market share a common prior about the initial value of a Gaussian hidden state, and learn about its subsequent values by observing a noisy public signal. The longrun 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 longrun 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 player'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.

Reputation Cycles and Earnings Dynamics

“…4.3.1). In dynamic games with type uncertainty of which ours is an example, Markovian equilibria also can entail fluctuating efforte.g., Board and Meyer-ter-Vehn (2013) and Cisternas (2018). With a risk averse agent, however, we show that the Holmström model acquires a Markovian, cyclical equilibrium: At each belief about the agent's quality, there are three Markov-equilibrium actions.…”

“…The market treatsas the signal. On path, i.e., when , -Because and are normal, the posterior is also normal: ' The posterior variance evolves deterministically as (5) and converges in the long-run to , whose value is obtained setting in so that 2…”

“…This additional inertia in the updating rule exactly compensates the direct impact on the variance of the signal, thus leaving consumption volatility unchanged. 5 In the remainder of the paper, we guarantee that expected returns are bounded by focusing on cases where ) .…”

Career Concerns and the Nature of Skills

“…This dependence is in fact the object of study of Cisternas (2018), where games of symmetric uncertainty about an exogenous state are analyzed. Importantly, these two papers are complementary.…”

“…Importantly, these two papers are complementary. First, in Cisternas (2018), learning is stationary, and hence, beliefs can be identified with posterior means. Reducing beliefs to a one-dimensional state, in turn, simplifies the task of proving the existence of Markov equilibria when nonlinearities are present.…”