# Interference Among First-Price Pacing Equilibria: A Bias and Variance Analysis

arXiv: https://arxiv.org/abs/2402.07322 · HTML: https://mlsanity.com/paper/2402.07322/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Feb 2024.

## Built on by (most cited first, 3 of 3)

- [Choosing Online Experiment Designs under Interference in Ads, Recommendations, and Member-Experience Systems](https://mlsanity.com/paper/2605.25290/) (2026)
- [Decision-Calibrated Conformal Uncertainty for Pacing Decisions in Streaming Advertising](https://mlsanity.com/paper/2606.10187/) (2026)
- [BAFF: Bid-Aware Filter Family for Mitigating Training Data Interference in RTB A/B Tests](https://mlsanity.com/paper/2609.08725/) (2026)

## Abstract (arXiv)

Online A/B testing is widely used in the internet industry to inform decisions on new feature roll-outs. For online marketplaces (such as advertising markets), standard approaches to A/B testing may lead to biased results when buyers operate under a budget constraint, as budget consumption in one arm of the experiment impacts performance of the other arm. To counteract this interference, one can use a budget-split design where the budget constraint operates on a per-arm basis and each arm receives an equal fraction of the budget, leading to ``budget-controlled A/B testing.'' Despite clear advantages of budget-controlled A/B testing, performance degrades when budget are split too small, limiting the overall throughput of such systems. In this paper, we propose a parallel budget-controlled A/B testing design where we use market segmentation to identify submarkets in the larger market, and we run parallel experiments on each submarket. Our contributions are as follows: First, we introduce and demonstrate the effectiveness of the parallel budget-controlled A/B test design with submarkets in a large online marketplace environment. Second, we formally define market interference in first-price auction markets using the first price pacing equilibrium (FPPE) framework. Third, we propose a debiased surrogate that eliminates the first-order bias of FPPE, drawing upon the principles of sensitivity analysis in mathematical programs. Fourth, we derive a plug-in estimator for the surrogate and establish its asymptotic normality. Fifth, we provide an estimation procedure for submarket parallel budget-controlled A/B tests. Finally, we present numerical examples on semi-synthetic data, confirming that the debiasing technique achieves the desired coverage properties.