Start a study of statistical inference and A/B testing of First-Price Pacing Equilibrium (FPPE). The FPPE model captures the dynamics resulting from large first-price auction markets where buyers use pacing-based budget control. Such a market occurs in the context of Internet advertising where budgets are common.
We propose a statistical framework for FPPE models. In this framework, a restricted FPPE with a continuum of items models the long-term steady-state behavior of an auction platform, providing data that an observable FPPE consisting of a finite number of items estimates. Restricted FPPE primitives, such as revenue, Nash social welfare (an unbiased measure of efficiency), and other parameters of interest. Develop the central limit theorem and asymptotically valid confidence intervals. Furthermore, we establish the asymptotic local minimax optimality of the estimator. We then use this theory to show that you can conduct statistically valid A/B tests on auction platforms. Numerical simulations verify the central limit theorem, and the empirical coverage of confidence intervals agrees with theory.