Learning Bayesian Nash Equilibrium in Auction Games via Approximate Best Response

Auction plays a crucial role in many modern trading environments, including online advertising and public resource allocation. As the number of competing bidders increases, learning Bayesian Nash Equilibrium (BNE) in auctions faces significant scalability challenges. Existing methods often experience slow convergence in large-scale auctions. For example, in a classic symmetric auction setting, the convergence rate depends on the number of bidders quadratically.To address this issue, we propose the Approximate Best Response Gradient method, a new approach for learning BNE efficiently in auction games. We leverage an analytic solution for gradient estimation to enable efficient gradient computation during optimization. Moreover, we introduce the Best Response Distance objective, which serves as an upper bound of approximation quality to BNE. By optimizing the new objective, our method is proven to achieve a local convergence rate independent of bidder numbers and circumvent the traditional quadratic complexity in the classic symmetric setting.Extensive experiments across various auction formats demonstrate that our approach accelerates convergence and enhances learning efficiency in complex auction settings.

When many buyers compete in auctions like those used in online advertising, finding a stable equilibrium, where each competitor reaches a strategic balance, becomes extremely difficult and slow to calculate. We developed a new approach that helps calculate these market equilibria much more efficiently. Our method uses mathematical insights to bypass the usual computational bottlenecks, significantly speeding up the solution process. This advancement will help better understand and predict auction behaviors in applications ranging from internet advertising to government resource allocation, providing valuable insights for both market designers and participants.