Providing Data Samples for Free

We consider the problem of a seller of data who sells information to a buyer regarding an unknown (to both parties) state of the world. Traditionally, the literature explores one-round strategies for selling information because of the seller's holdup problem: once a portion of the data set is released, the buyer's estimate improves, and as a result, the value of the remaining data set drops. In this paper, we show that this intuition is true when the buyer's objective is to improve the precision of the estimate. On the other hand, we establish that when the buyer's objective is to improve downstream operational decisions (e.g., better pricing decisions in a market with unknown elasticity) and when the buyer's initial estimate is misspecified, one-round strategies are outperformed by selling strategies that initially provide free samples. In particular, we provide conditions under which such free-sample strategies generate strictly higher revenues than static strategies and illustrate the benefit of providing data samples for free through a series of examples. Furthermore, we characterize the optimal dynamic pricing strategy within the class of strategies that provide samples over time (at a constant rate), charging a flow price until some time when the rest of the data set is released at a lump-sum amount.