While users claim to be concerned about privacy, often they do little to protect their privacy in their online actions. One prominent explanation for this "privacy paradox" is that when an individual shares her data, it is not just her privacy that is compromised; the privacy of other individuals with correlated data is also compromised. This information leakage encourages oversharing of data and significantly impacts the incentives of individuals in online platforms. In this paper, we study the design of mechanisms for data acquisition in settings with information leakage and verifiable data. We design an incentive compatible mechanism that optimizes the worst-case trade-off between bias and variance of the estimation subject to a budget constraint, where the worst-case is over the unknown correlation between costs and data. Additionally, we characterize the structure of the optimal mechanism in closed form and study monotonicity and non-monotonicity properties of the marketplace.

翻译：虽然用户声称对隐私感到担忧,但他们往往在网上行动中对保护隐私无动于衷。 这种“隐私悖论”的一个突出解释是,当个人分享其数据时,不仅她的隐私受到损害;拥有相关数据的其他个人的隐私也受到损害。这种信息泄漏鼓励了数据共享过度,严重影响了在线平台上个人的积极性。在本文中,我们研究了在信息泄漏和可核实数据的情况下数据获取机制的设计。我们设计了一个奖励兼容机制,优化了受预算制约的估算偏差和差异之间的最坏的权衡,因为最坏的情况是成本和数据之间存在未知的关联。此外,我们用封闭的形式描述最佳机制的结构,研究市场中的单一性和非流动特性。