We study dynamic signaling when the informed party does not observe the signals generated by her actions. A forward-looking sender signals her type continuously over time to a myopic receiver who privately monitors her behavior; in turn, the receiver transmits his private inferences back through an imperfect public signal of his actions. Preferences are linear-quadratic and the information structure is Gaussian. We construct linear Markov equilibria using belief states up to the sender’s second-order belief. Because of the private monitoring, this state is an explicit function of the sender’s past play, leading to a novel separation effect through the second-order belief channel. Applications to models of organizations and reputation are examined.
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.
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.
I examine how career concerns are shaped by the nature of productive actions taken by workers. A worker’s skills follow a Gaussian process with an endogenous component reflecting human-capital accumulation. Effort and skills are substitutes both in the output process (as in Holmstrom 1999) and in the skills technology. The focus is on deterministic equilibria by virtue of Gaussian learning. When effort and skills are direct inputs to production and skills are exogenous, effort can be inefficiently high in the beginning of a career. In contrast, when skills are the only input to production but accumulate through past effort choices, the worker always underinvests in skill acquisition. At the center of the discrepancy are two types of ex post errors that arise at interpreting output due to an identification problem faced by the market. Finally, the robustness of the underinvestment result is explored via variations in the skill-accumulation technology and in the information structure, and policy implications are discussed.