# Pacing Equilibrium in First-Price Auction Markets

arXiv: https://arxiv.org/abs/1811.07166 · HTML: https://mlsanity.com/paper/1811.07166/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Nov 2018.

## Built on by (most cited first, 14 of 14)

- [Stochastic Bandits for Multi-platform Budget Optimization in Online Advertising](https://mlsanity.com/paper/2103.10246/) (2021)
- [Autobidders with Budget and ROI Constraints: Efficiency, Regret, and Pacing Dynamics](https://mlsanity.com/paper/2301.13306/) (2023)
- [Online Bidding Algorithms for Return-on-Spend Constrained Advertisers](https://mlsanity.com/paper/2208.13713/) (2022)
- [Learning to Bid in Non-Stationary Repeated First-Price Auctions](https://mlsanity.com/paper/2501.13358/) (2025)
- [Optimal Spend Rate Estimation and Pacing for Ad Campaigns with Budgets](https://mlsanity.com/paper/2202.05881/) (2022)
- [Multi-Platform Budget Management in Ad Markets with Non-IC Auctions](https://mlsanity.com/paper/2306.07352/) (2023)
- [A Real-World Implementation of Unbiased Lift-based Bidding System](https://mlsanity.com/paper/2202.13868/) (2022)
- [Dynamic Budget Throttling in Repeated Second-Price Auctions](https://mlsanity.com/paper/2207.04690/) (2022)
- [Pairwise Ranking Losses of Click-Through Rates Prediction for Welfare Maximization in Ad Auctions](https://mlsanity.com/paper/2306.01799/) (2023)
- [Learning to Bid with Unknown Private Values in Budget-Constrained First-Price Auctions](https://mlsanity.com/paper/2605.09448/) (2026)
- [Model Monotonicity in Autobidding Auctions: When Do Better Predictions Lead to Better Outcomes?](https://mlsanity.com/paper/2605.31036/) (2026)
- [Large-Scale Contextual Market Equilibrium Computation through Deep Learning](https://mlsanity.com/paper/2406.15459/) (2024)
- [Large-Scale Auto-bidding with Nash Equilibrium Constraints](https://mlsanity.com/paper/2503.10304/) (2025)
- [Constrained Auto-Bidding via Generative Response Modeling](https://mlsanity.com/paper/2605.27811/) (2026)

## Abstract (arXiv)

Mature internet advertising platforms offer high-level campaign management tools to help advertisers run their campaigns, often abstracting away the intricacies of how each ad is placed and focusing on aggregate metrics of interest to advertisers. On such platforms, advertisers often participate in auctions through a proxy bidder, so the standard incentive analyses that are common in the literature do not apply directly. In this paper, we take the perspective of a budget management system that surfaces aggregated incentives -- instead of individual auctions -- and compare first and second price auctions. We show that theory offers surprising endorsement for using a first price auction to sell individual impressions. In particular, first price auctions guarantee uniqueness of the steady-state equilibrium of the budget management system, monotonicity, and other desirable properties, as well as efficient computation through the solution to the well-studied Eisenberg-Gale convex program. Contrary to what one can expect from first price auctions, we show that incentives issues are not a barrier that undermines the system. Using realistic instances generated from data collected at real-world auction platforms, we show that bidders have small regret with respect to their optimal ex-post strategy, and they do not have a big incentive to misreport when they can influence equilibria directly by giving inputs strategically. Finally, budget-constrained bidders, who have significant prevalence in real-world platforms, tend to have smaller regrets. Our computations indicate that bidder budgets, pacing multipliers and regrets all have a positive association in statistical terms.