We study a three-layer data market comprising users (data owners), platforms, and a data buyer. Each user benefits from platform services in exchange for data, incurring privacy loss when their data, albeit noisily, is shared with the buyer. The user chooses platforms to share data with, while platforms decide on data noise levels and pricing before selling to the buyer. The buyer selects platforms to purchase data from. We model these interactions via a multi-stage game, focusing on the subgame Nash equilibrium. We find that when the buyer places a high value on user data (and platforms can command high prices), all platforms offer services to the user who joins and shares data with every platform. Conversely, when the buyer's valuation of user data is low, only large platforms with low service costs can afford to serve users. In this scenario, users exclusively join and share data with these low-cost platforms. Interestingly, increased competition benefits the buyer, not the user: as the number of platforms increases, the user utility does not necessarily improve while the buyer utility improves. However, increasing the competition improves the overall utilitarian welfare. Building on our analysis, we then study regulations to improve the user utility. We discover that banning data sharing maximizes user utility only when all platforms are low-cost. In mixed markets of high- and low-cost platforms, users prefer a minimum noise mandate over a sharing ban. Imposing this mandate on high-cost platforms and banning data sharing for low-cost ones further enhances user utility.

翻译：我们研究了一个包含用户（数据所有者）、平台和数据买家的三层数据市场。用户通过提供数据换取平台服务，但数据（即便经过加噪处理）与买家共享会导致隐私损失。用户自主选择与哪些平台共享数据，平台则自行决定数据加噪水平及定价策略，随后向买家出售数据。买家则从平台中选择购买数据的对象。我们通过多阶段博弈模型刻画这些互动关系，重点分析子博弈纳什均衡。研究发现：当买家对用户数据的估价较高（平台可制定高价）时，所有平台都会向用户提供服务，用户也将加入所有平台并与之共享数据。反之，当买家对用户数据的估价较低时，仅有服务成本低的大型平台能够承担服务成本。在此情形下，用户将仅加入这些低成本平台并与之共享数据。值得注意的是，竞争加剧有利于买家而非用户：随着平台数量增加，用户效用未必提升，但买家效用必然改善。然而，竞争加剧会提升整体社会福利。基于分析，我们进一步研究了提升用户效用的监管措施。研究发现：仅在所有平台均为低成本时，禁止数据共享才能实现用户效用最大化。在低成本与高成本平台并存的混合市场中，用户更倾向于最低加噪要求而非全面禁止共享。对高成本平台实施最低加噪要求、对低成本平台禁止数据共享的差异化政策，可进一步优化用户效用。