# Large-Scale Auto-bidding with Nash Equilibrium Constraints

arXiv: https://arxiv.org/abs/2503.10304 · HTML: https://mlsanity.com/paper/2503.10304/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 36 references that are in the map.
- First posted on arXiv 13 Mar 2025.

## Builds on (most cited first, 18 of 18)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Multi-Agent Actor-Critic for Mixed Cooperative-Competitive Environments](https://mlsanity.com/paper/1706.02275/) (2017)
- [Real-Time Bidding by Reinforcement Learning in Display Advertising](https://mlsanity.com/paper/1701.02490/) (2017)
- [Real-Time Bidding with Multi-Agent Reinforcement Learning in Display Advertising](https://mlsanity.com/paper/1802.09756/) (2018)
- [Budget Constrained Bidding by Model-free Reinforcement Learning in Display Advertising](https://mlsanity.com/paper/1802.08365/) (2018)
- [Sustainable Online Reinforcement Learning for Auto-bidding](https://mlsanity.com/paper/2210.07006/) (2022)
- [AuctionNet: A Novel Benchmark for Decision-Making in Large-Scale Games](https://mlsanity.com/paper/2412.10798/) (2024)
- [A Cooperative-Competitive Multi-Agent Framework for Auto-bidding in Online Advertising](https://mlsanity.com/paper/2106.06224/) (2021)
- [Autobidders with Budget and ROI Constraints: Efficiency, Regret, and Pacing Dynamics](https://mlsanity.com/paper/2301.13306/) (2023)
- [Multiplicative Pacing Equilibria in Auction Markets](https://mlsanity.com/paper/1706.07151/) (2017)
- [Pacing Equilibrium in First-Price Auction Markets](https://mlsanity.com/paper/1811.07166/) (2018)
- [Specification-Guided Learning of Nash Equilibria with High Social Welfare](https://mlsanity.com/paper/2206.03348/) (2022)
- [Efficiency of the First-Price Auction in the Autobidding World](https://mlsanity.com/paper/2208.10650/) (2022)
- [The Complexity of Pacing for Second-Price Auctions](https://mlsanity.com/paper/2103.13969/) (2021)
- [Maximizing Nash Social Welfare in 2-Value Instances](https://mlsanity.com/paper/2107.08965/) (2021)
- [Incrementality Bidding via Reinforcement Learning under Mixed and Delayed Rewards](https://mlsanity.com/paper/2206.01293/) (2022)
- [Complex Dynamics in Autobidding Systems](https://mlsanity.com/paper/2406.19350/) (2024)
- [Auto-bidding in real-time auctions via Oracle Imitation Learning (OIL)](https://mlsanity.com/paper/2412.11434/) (2024)

## Abstract (arXiv)

Auto-bidding has become a cornerstone of modern online advertising platforms, enabling many advertisers to automate bidding at scale and optimize campaign performance. However, prevailing industrial systems rely on single-agent auto-bidding methods that are scalable but overlook the strategic interdependence among advertisers' bids, leading to unstable or suboptimal outcomes. While recent works recognize the game-theoretic nature of auto-bidding, existing approaches remain either computationally intractable at scale or lack a principled equilibrium-selection that aligns with platform-wide objectives. In this paper, we bridge this gap by introducing Nash Equilibrium-Constrained Bidding (NCB), a principled and scalable auto-bidding framework that recasts auto-bidding as a platform-wide optimization problem subject to Nash equilibrium constraints. This approach accounts for fine-grained strategic interdependencies among advertisers, ensuring both agent-level stability and ecosystem-level optimality. Notably, we develop a theoretically sound penalty-based primal-dual gradient method with rigorous convergence guarantees, supported by an efficient algorithm suitable for industrial deployment. Extensive experiments validate the effectiveness of our approach.