Signaling in Data Markets via Free Samples

We study a setting in which a data buyer seeks to estimate an unknown parameter by purchasing samples from one of $K$ data sellers. Each seller has privately known data quality (e.g., high vs. low variance) and a private per-sample cost. We consider a multi-stage game in which the first stage is a free-trial stage in which the sellers have the option of signaling data quality by offering a few samples of data for free. Buyers update their beliefs based on the sample variance of the free data and then run a procurement auction to buy data in a second stage. For the auction stage, we characterize an approximately optimal Bayesian incentive compatible mechanism: the buyer selects a single seller by minimizing a belief-adjusted virtual cost and chooses the purchased sample size as a function of posterior quality and virtual cost. For the free-trial stage, we characterize the equilibrium, taking the above mechanism as the continuation game. Free trials may fail to emerge: for some parameters, all sellers reveal zero samples. However, under sufficiently strong competition (large $K$), there is an equilibrium in which sellers reveal the maximum allowable number of samples; in fact, it is the unique equilibrium.