We study a data marketplace where a broker intermediates between buyers, who seek to estimate the mean \(μ\) of an unknown normal distribution \(\Ncal(μ, σ^2)\), and contributors, who can collect data from this distribution at a cost. The broker delegates data collection work to contributors, aggregates reported datasets, sells it to buyers, and redistributes revenue as payments to contributors. We aim to maximize welfare or profit under key constraints: individual rationality for buyers and contributors, incentive compatibility (contributors are incentivized to comply with data collection instructions and truthfully report the collected data), and budget balance (total contributor payments equals total revenue). We first compute welfare/profit-optimal prices under truthful reporting; however, to incentivize data collection and truthful data reporting, we adjust them based on discrepancies in contributors' reported data. This yields a Nash equilibrium (NE) where the two lowest-cost contributors collect all data. We complement this with two hardness results: \emph{(i)} no nontrivial dominant-strategy incentive-compatible mechanism exists in this problem, and \emph{(ii)} no mechanism outperforms ours in a NE.

翻译：我们研究一个数据市场，其中中介机构协调买方和贡献者之间的关系：买方希望估计未知正态分布 \(\Ncal(μ, σ^2)\) 的均值 \(μ\)，而贡献者可以采集该分布的数据并承担相应成本。中介将数据采集工作委托给贡献者，汇总报告的数据集后出售给买方，并将收入作为报酬分配给贡献者。我们的目标是在以下关键约束下最大化社会福利或利润：买方和贡献者的个体理性、激励相容性（激励贡献者遵守数据采集指令并如实报告所采集数据），以及预算平衡（贡献者所得总报酬等于总收入）。首先，我们在数据真实报告的条件下计算出福利/利润最优定价；然而，为了激励数据采集和数据真实报告，我们根据贡献者报告数据的差异对这些定价进行调整。由此得到一个纳什均衡（NE），在该均衡中，成本最低的两位贡献者采集所有数据。我们还给出两个难度结果：\emph{（i）}在该问题中不存在任何非平凡的占优策略激励相容机制；\emph{（ii）}在纳什均衡下，没有任何机制能比我们的机制更优。