The $\textit{data market design}$ problem is a problem in economic theory to find a set of signaling schemes (statistical experiments) to maximize expected revenue to the information seller, where each experiment reveals some of the information known to a seller and has a corresponding price [Bergemann et al., 2018]. Each buyer has their own decision to make in a world environment, and their subjective expected value for the information associated with a particular experiment comes from the improvement in this decision and depends on their prior and value for different outcomes. In a setting with multiple buyers, a buyer's expected value for an experiment may also depend on the information sold to others [Bonatti et al., 2022]. We introduce the application of deep learning for the design of revenue-optimal data markets, looking to expand the frontiers of what can be understood and achieved. Relative to earlier work on deep learning for auction design [D\"utting et al., 2023], we must learn signaling schemes rather than allocation rules and handle $\textit{obedience constraints}$ $-$ these arising from modeling the downstream actions of buyers $-$ in addition to incentive constraints on bids. Our experiments demonstrate that this new deep learning framework can almost precisely replicate all known solutions from theory, expand to more complex settings, and be used to establish the optimality of new designs for data markets and make conjectures in regard to the structure of optimal designs.

翻译：$\textit{数据市场设计}$问题是经济学理论中的一个问题，旨在寻找一组信号机制（统计实验）以最大化信息卖方的预期收益，其中每个实验揭示卖方已知的部分信息并对应一个价格[Bergemann et al., 2018]。每个买方在特定世界环境中做出自己的决策，他们对特定实验相关信息的主观预期价值来自于决策的改进，并取决于其先验信念和对不同结果的估值。在多个买方共存的情况下，买方对某一实验的预期价值还可能取决于出售给其他买方的信息[Bonatti et al., 2022]。我们引入深度学习方法来设计收益最优的数据市场，旨在拓展可理解与可实现的边界。与早期关于深度学习在拍卖设计中的应用研究相比[Dütting et al., 2023]，我们需要学习的不是分配规则而是信号机制，并需处理$\textit{顺从约束}$——这些约束源于对买方后续行动的建模——以及针对投标的激励约束。我们的实验表明，这一新的深度学习框架几乎能精确复现理论中所有已知解，可扩展至更复杂的场景，并能用于确立数据市场新设计的最优性，以及提出关于最优设计结构的猜想。