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 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.

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A common force driving many productive decisions by workers is the possibility of being perceived as skilled in a certain area of expertise. While such career concerns are a defining feature of many occupations, new technologies that facilitate the flow of information about potential employees, as well as online marketplaces that enable matches between firms and workers, naturally lead these motives to play an even more predominant role nowadays. Studying how markets reward ability is a relevant topic for two reasons. First, it helps to uncover the mechanisms through which workers can build their reputations in labor markets. Second, it helps to evaluate whether market-based incentives induce appropriate productive decisions by workers, thereby contributing to the discussion of economic policy.In traditional models of career concerns (e.g., Holmström 1999; Dewatripont, Jewitt, and Tirole 1999; and Bonatti and Hörner 2017), reputation is understood as a market's belief concerning a worker's unobserved measure of productive ability modeled as an exogenous type (e.g., "talent," either fixed or stochastically evolving over time); the worker's action (e.g., "effort") is in turn a direct input to