Equilibrium Learning in Combinatorial Auctions: Computing Approximate Bayesian Nash Equilibria via Pseudogradient Dynamics

TL;DR

This paper introduces a scalable neural network-based method for approximating Bayesian Nash equilibria in combinatorial auctions using pseudogradient dynamics, addressing computational challenges and demonstrating robust convergence.

Contribution

It proposes a novel equilibrium learning approach that leverages neural networks and pseudogradients, providing a practical alternative to PDE solutions and best-response calculations.

Findings

Fast convergence to approximate BNE in various auction types

Method is scalable and robust across different auction settings

Provides a sufficient condition for convergence

Abstract

Applications of combinatorial auctions (CA) as market mechanisms are prevalent in practice, yet their Bayesian Nash equilibria (BNE) remain poorly understood. Analytical solutions are known only for a few cases where the problem can be reformulated as a tractable partial differential equation (PDE). In the general case, finding BNE is known to be computationally hard. Previous work on numerical computation of BNE in auctions has relied either on solving such PDEs explicitly, calculating pointwise best-responses in strategy space, or iteratively solving restricted subgames. In this study, we present a generic yet scalable alternative multi-agent equilibrium learning method that represents strategies as neural networks and applies policy iteration based on gradient dynamics in self-play. Most auctions are ex-post nondifferentiable, so gradients may be unavailable or misleading, and we rely on suitable pseudogradient estimates instead. Although it is well-known that gradient dynamics cannot guarantee convergence to NE in general, we observe fast and robust convergence to approximate BNE in a wide variety of auctions and present a sufficient condition for convergence