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.

翻译：自动竞价已成为现代在线广告平台的基石，使众多广告主能够大规模自动化出价并优化广告活动效果。然而，当前主流工业系统依赖单智能体自动竞价方法，虽具备可扩展性，却忽视了广告主出价间的策略相互依赖性，导致不稳定或次优的结果。尽管近期研究认识到自动竞价的博弈论本质，现有方法要么在大规模场景下计算不可行，要么缺乏与平台全局目标一致的原则性均衡选择机制。本文通过引入纳什均衡约束竞价框架，弥补了这一空白：该原则化且可扩展的自动竞价框架将自动竞价重构为受纳什均衡约束的平台全局优化问题。该方法充分考虑了广告主间细粒度的策略相互依赖性，同时保障了智能体层面的稳定性与生态系统层面的最优性。特别地，我们提出了一种理论严谨的基于惩罚项的原对偶梯度方法，该方法具有严格的收敛性保证，并辅以适合工业部署的高效算法支持。大量实验验证了我们方法的有效性。