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.
We consider learning and signaling 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. This can be explained by decomposing incentives into signaling and learning, and discuss implications for prices, quantities, and welfare.
We characterize the optimal mechanism and investment level in an environment where (i) two projects of independent costs are purchased sequentially, (ii) the buyer can commit to a two‐period mechanism, and (iii) the winner of the first project can invest in a cost‐reducing technology between auctions. We show that, in an attempt to induce more competition in the first period, the optimal mechanism gives an advantage to the first‐period winner in the second auction. As a result of this advantage, the first‐period winner invests more than the socially efficient level. Optimal advantages, therefore, create two different channels for cost minimization in buyer‐supplier relationships.