Sequential Information Selling: Perfect Price Discrimination and the Role of Encryption

We study a dynamic game in which a monopolistic seller sequentially discloses information about a binary state to a consumer through priced experiments. The consumer privately observes a binary signal which influences her willingness to pay for information. We show that if buyer types favor different actions but their willingness to pay for a state-revealing test is sufficiently close, then the seller can commit to a sequence of priced experiments that extracts the entire surplus of both consumer types simultaneously. The optimal sequence of experiments is such that the high-valuation type assigns a higher probability to outcomes that trigger further information acquisition, thus creating a difference in expected costs. As a key element of the construction, we introduce an ‘encryption protocol’ under which the consumer faces a stopping problem. We then characterize situations in which the seller strictly benefits from a dynamic selling strategy when perfect price discrimination is not feasible. Finally, we illustrate our framework in the context of medical diagnostic testing, showing that a free test followed by a state-revealing test is often sufficient to improve revenue in comparison with a static approach.