Statistical Inference and A/B Testing for First-Price Pacing Equilibria

TL;DR

This paper develops a statistical inference framework for first-price pacing equilibria in large-scale auction markets, enabling reliable estimation and A/B testing for internet advertising platforms.

Contribution

It introduces a novel statistical framework for FPPE, including limit models, estimators, confidence intervals, and A/B testing methods with proven optimality.

Findings

Central limit theorems for estimators

Asymptotic confidence intervals are valid

Numerical simulations confirm theoretical results

Abstract

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.