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.

翻译：本文研究了一种场景：数据购买方希望通过从K个数据卖方之一购买样本来估计未知参数。每个卖方拥有私有已知的数据质量（例如高方差与低方差）以及私有单位样本成本。我们构建了一个多阶段博弈模型，其中第一阶段为免费试用阶段：卖方可通过提供少量免费数据样本来传递数据质量信号。购买方根据免费数据的样本方差更新其信念，随后在第二阶段通过采购拍卖购买数据。针对拍卖阶段，我们刻画了一种近似最优的贝叶斯激励相容机制：购买方通过最小化信念调整虚拟成本来选择单一卖方，并根据后验质量与虚拟成本函数确定采购样本量。针对免费试用阶段，我们将上述机制作为后续博弈，刻画了均衡状态。免费试用可能无法实现：在某些参数条件下，所有卖方均选择零样本披露。然而，在充分竞争条件下（K值较大），存在卖方披露最大允许样本数的均衡；事实上，该均衡具有唯一性。