Interference Among First-Price Pacing Equilibria: A Bias and Variance Analysis
<|reference_start|>Interference Among First-Price Pacing Equilibria: A Bias and Variance Analysis: 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.<|reference_end|>
@article{liao2024interference,
    title={Interference Among First-Price Pacing Equilibria: A Bias and Variance
  Analysis},
    author={Luofeng Liao and Christian Kroer and Sergei Leonenkov and Okke
  Schrijvers and Liang Shi and Nicolas Stier-Moses and Congshan Zhang},
    journal={arXiv preprint arXiv:2402.07322},
    year={2024},
    archivePrefix={arXiv},
    eprint={2402.07322},
    primaryClass={math.ST cs.GT econ.EM stat.TH}
}