Consumer Scores and Price Discrimination (vol 87, pg 750, 2020)

A long-lived consumer interacts with a sequence of firms in a stationary Gaussian setting. Each firm relies on the consumer's current score--an aggregate measure of past quantity signals discounted exponentially--to learn about her preferences and to set prices. In the unique stationary linear Markov equilibrium, the consumer reduces her demand to drive average prices below the no-information benchmark. The firms' learning is maximized by persistent scores, i.e., scores that overweigh past information relative to Bayes' rule when observing disaggregated data. Hidden scores--those only observed by firms--reduce demand sensitivity, increase expected prices, and reduce expected quantities.