We initiate the study of statistical inference and A/B testing for first-price pacing equilibria (FPPE). The FPPE model captures the dynamics resulting from large-scale first-price auction markets where buyers use pacing-based budget management. Such markets arise in the context of internet advertising, where budgets are prevalent. We propose a statistical framework for the FPPE model, in which a limit FPPE with a continuum of items models the long-run steady-state behavior of the auction platform, and an observable FPPE consisting of a finite number of items provides the data to estimate primitives of the limit FPPE, such as revenue, Nash social welfare (a fair metric of efficiency), and other parameters of interest. We develop central limit theorems and asymptotically valid confidence intervals. Furthermore, we establish the asymptotic local minimax optimality of our estimators. We then show that the theory can be used for conducting statistically valid A/B testing on auction platforms. Numerical simulations verify our central limit theorems, and empirical coverage rates for our confidence intervals agree with our theory.

翻译：本文首次研究了第一价格预算均衡（FPPE）的统计推断与A/B测试问题。FPPE模型刻画了大规模第一价格拍卖市场中，买家采用预算管理策略时的动态过程。这类市场常见于存在预算约束的互联网广告领域。我们为FPPE模型提出了一套统计框架：其中，包含连续物品的极限FPPE刻画了拍卖平台的长期稳态行为，而由有限物品构成的可观测FPPE则提供数据，用以估计极限FPPE的基本参数（如收益、纳什社会福利——一种衡量公平性的效率指标）及其他关注参数。我们推导了中心极限定理并建立了渐近有效的置信区间，进一步证明了估计量的渐近局部极小极大最优性。随后展示该理论可用于在拍卖平台上开展统计有效的A/B测试。数值模拟验证了中心极限定理，经验置信区间覆盖率与理论结果一致。