Large-Scale Auto-bidding with Nash Equilibrium Constraints

Abstract

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.