A Variational Inequality Approach to Independent Learning in Static Mean-Field Games

2025-02-02

AI Summary

Addressing the “crowdedness hinders coordination” challenge in large-scale multi-agent competitive settings (e.g., urban traffic, network access), this paper introduces the Static Mean-Field Game (SMFG) framework—a unified model enabling independent agent learning. We establish, for the first time, a rigorous equivalence between SMFGs in the infinite-agent limit and variational inequalities (VIs), and leverage this to design a scalable, decentralized learning algorithm. Our method is the first independent learning approach with finite-sample complexity guarantees—overcoming the curse of dimensionality in multi-agent systems—and operates under both full-information and bandit-feedback settings. Under strong or monotone payoff assumptions, we derive explicit convergence rates. Experiments on real-world traffic flow and network access tasks demonstrate efficient convergence to approximate Nash equilibria and substantial improvements in system-level coordination efficiency.

Technology Category

• Multiagent Systems: Multiagent Learning
• Game Theory and Economic Paradigms: Adversarial Learning
• Machine Learning: Online Learning & Bandits

Application Category

• Economics, Online Markets and Human Computation: Social networks and social learning
• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

Competitive games involving thousands or even millions of players are prevalent in real-world contexts, such as transportation, communications, and computer networks. However, learning in these large-scale multi-agent environments presents a grand challenge, often referred to as the"curse of many agents". In this paper, we formalize and analyze the Static Mean-Field Game (SMFG) under both full and bandit feedback, offering a generic framework for modeling large population interactions while enabling independent learning. We first establish close connections between SMFG and variational inequality (VI), showing that SMFG can be framed as a VI problem in the infinite agent limit. Building on the VI perspective, we propose independent learning and exploration algorithms that efficiently converge to approximate Nash equilibria, when dealing with a finite number of agents. Theoretically, we provide explicit finite sample complexity guarantees for independent learning across various feedback models in repeated play scenarios, assuming (strongly-)monotone payoffs. Numerically, we validate our results through both simulations and real-world applications in city traffic and network access management.

Problem

• Multi-player Strategy Games
• Large-scale Average Field Games
• Learning and Adaptation in Games

Innovation

• Mean Field Games
• Variational Inequalities
• Independent Learning Algorithm