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 its 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 an ordinary differential equation to characterize equilibrium behavior in which the long-run player’s actions depend on the history of the game only through the market’s correct belief. Using these conditions, I demonstrate the existence of pure-strategy equilibria in Markov 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.

We study the implications of aggregating consumers’ purchase histories into scores that proxy for unobserved willingness to pay. A long-lived consumer interacts with a sequence of firms. Each firm relies on the consumer’s current score–a linear aggregate of noisy purchase signals—to learn about her preferences and to set prices. If the consumer is strategic, she reduces her demand to manipulate her score, which reduces the average equilibrium price. Firms in turn prefer scores that overweigh past signals relative to applying Bayes’ rule with disaggregated data, as this mitigates the ratchet effect and maximizes the firms’ ability to price discriminate. Consumers with high average willingness to pay benefit from data collection, because the gains from low average prices dominate the losses from price discrimination. Finally, hidden scores—those only observed by the firms—reduce demand sensitivity, increase average prices, and reduce consumer surplus, sometimes below the naive-consumer level.

We study dynamic signalling when the sender does not see the signals that her actions generate. The sender then uses her past play to forecast what a receiver believes, in turn forcing the receiver to forecast the previous forecast, and so forth. We identify a class of linear-quadratic-Gaussian games where this endogenous higher-order uncertainty can be handled. The sender’s second-order belief is key: it is a private state that she controls, and it creates a new channel for information transmission. We examine the role of higher-order uncertainty and this new signalling channel in applications to macroeconomics, reputation, and trading: inflationary biases under discretion can be larger; career-concerned agents may benefit from not knowing their reputations; and informed trades can carry more price impact. We also introduce an existence method for boundary value problems that can be used in other dynamic games.

We consider learning and signalling in a dynamic Cournot oligopoly where firms have private information about their production costs and only observe the market price, which is subject to unobservable demand shocks. An equilibrium is Markov if play depends on the history only through the firms’ beliefs about costs and calendar time. We characterize symmetric linear Markov equilibria as solutions to a boundary value problem. In every such equilibrium, given a long enough horizon, play converges to the static complete information outcome for the realized costs, but each firm only learns its competitors’ average cost. The weights assigned to costs and beliefs under the equilibrium strategies are non-monotone over time. We explain this by decomposing incentives into signalling and learning, and discuss implications for prices, quantities, and welfare.

We propose a theory of coordination and influence among blockholders. Privately informed activists time their trades in sequence to lower acquisition costs, prompting a strategic use of order flows: leader activists create trading gains for their followers, ultimately influencing their willingness to bear greater value‐enhancing intervention costs. Through this channel, informed trades can exhibit predictability, in sharp contrast with Kyle (1985, Econometrica 53, 1315–1335). We explain how this novel predictability shapes free‐rider problems affecting governance, and how it produces price abnormalities analogous to those documented empirically. We also uncover how private information interdependence can be a key catalyst for the mechanism studied.