Motivated by the problem of selling large, proprietary data, we consider an information pricing problem proposed by Bergemann et al. that involves a decision-making buyer and a monopolistic seller. The seller has access to the underlying state of the world that determines the utility of the various actions the buyer may take. Since the buyer gains greater utility through better decisions resulting from more accurate assessments of the state, the seller can therefore promise the buyer supplemental information at a price. To contend with the fact that the seller may not be perfectly informed about the buyer's private preferences (or utility), we frame the problem of designing a data product as one where the seller designs a revenue-maximizing menu of statistical experiments. Prior work by Cai et al. showed that an optimal menu can be found in time polynomial in the state space, whereas we observe that the state space is naturally exponential in the dimension of the data. We propose an algorithm which, given only sampling access to the state space, provably generates a near-optimal menu with a number of samples independent of the state space. We then analyze a special case of high-dimensional Gaussian data, showing that (a) it suffices to consider scalar Gaussian experiments, (b) the optimal menu of such experiments can be found efficiently via a semidefinite program, and (c) full surplus extraction occurs if and only if a natural separation condition holds on the set of potential preferences of the buyer.

翻译：受销售大规模专有数据问题的启发，我们研究了Bergemann等人提出的信息定价问题，该问题涉及一个决策型买家和一个垄断型卖家。卖家能够获取决定买家各种行动效用的世界底层状态。由于买家通过更准确的状态评估做出更好的决策从而获得更高效用，因此卖家可以向买家承诺以一定价格提供补充信息。针对卖家可能无法完全了解买家私人偏好（或效用）这一现实情况，我们将数据产品的设计问题框架化为卖家设计一个收益最大化的统计实验菜单。Cai等人的先前研究表明，最优菜单可以在状态空间的多项式时间内求得，而我们观察到状态空间在数据维度上自然呈指数级增长。我们提出了一种算法，该算法仅需对状态空间进行采样访问，就能以与状态空间无关的样本数量生成近乎最优的菜单。随后，我们分析了高维高斯数据这一特例，表明：(a) 仅考虑标量高斯实验就足够了，(b) 此类实验的最优菜单可以通过半定规划高效求解，(c) 当且仅当买家潜在偏好集满足某种自然分离条件时，才能实现完全的剩余提取。