非线性定价恢复数据卖方的可计算性
Non-Linear Pricing Restores Tractability for a Data Seller
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- University of Illinois, Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
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中文总结 AI 辅助
本研究探讨数据卖方在预算受限买方下设计定价机制，发现允许非线性定价不仅能增加收入，还能恢复计算可处理性，最优定价具有分段线性凸结构，且拐点数量受买方数量限制。
中文摘要 AI 辅助
我们考虑一个数据卖方，其设计针对多个数据集的定价机制，以从预算受限的买方那里最大化收入。卖方提供多个数据集，并为每个数据集分配一个定价函数，该函数将购买数量映射到总支付。目标是设计这些定价函数以最大化收入，预期买方——他们在准确度提升与成本之间进行权衡——在预算约束下最优地选择捆绑包。先前的工作[Chaudhury等人，2026]在限制每个数据集被分配线性价格的条件下研究了这种最优定价，并表明计算最优线性价格在计算上是难处理的。相反，我们允许每个数据集通过一般函数定价，并表明这种额外的灵活性不仅能增加收入，还能恢复可计算性，从而在经济表现和计算效率上产生令人惊讶的同时改进。即使定价函数仅要求单调且下半连续，最优定价也呈现出高度结构化和简单的形式：每个定价函数是分段线性和凸的（PLC），并且最优解可以在多项式时间内计算。此外，所有定价函数中拐点的总数受买方数量的限制。因此，当数据集数量显著超过买方数量时，大多数定价函数实际上是线性的。我们进一步通过分析拐点数量以及在一个从真实数据集生成的模拟上最优非线性定价与最优线性定价之间的收入差距，实证研究了最优定价的结构。
英文摘要
We consider a data seller who designs pricing mechanisms over multiple datasets to maximize revenue from budget-constrained buyers. The seller offers multiple datasets and assigns each a pricing function that maps the quantity purchased to a total payment. The goal is to design these pricing functions to maximize revenue, anticipating that buyers---who trade off accuracy gains against cost---choose bundles optimally subject to their budget constraints. Prior work [Chaudhury et al., 2026] studies such optimal pricing under the restriction that each dataset is assigned a linear price, and shows that computing optimal linear prices is computationally intractable. In contrast, we allow each dataset to be priced via a general function and show that this additional flexibility can not only increase the revenue but also restore tractability, yielding a surprising simultaneous improvement in economic performance and computational efficiency. Even when pricing functions are only required to be monotone and lower-continuous, optimal pricing admits a highly structured and simple form: each pricing function is piecewise linear and convex (PLC), and the optimal solution can be computed in polynomial time. Moreover, the total number of kinks across all pricing functions is bounded by the number of buyers. Consequently, when datasets significantly outnumber buyers, most pricing functions are effectively linear. We further empirically study the structure of optimal pricing by analyzing the number of kinks and the revenue gap between optimal nonlinear pricing and optimal linear pricing on simulations generated from a real dataset.
