Learning Large-Scale Competitive Team Behaviors with Mean-Field Interactions

Abstract

While multi-agent reinforcement learning (MARL) has been proven effective across both collaborative and competitive tasks, existing algorithms often struggle to scale to large populations of agents. Recent advancements in mean-field (MF) theory provide scalable solutions by approximating population interactions as a continuum, yet most existing frameworks focus exclusively on either fully cooperative or purely competitive settings. To bridge this gap, we introduce MF-MAPPO, a mean-field extension of PPO designed for zero-sum team games that integrate intra-team cooperation with inter-team competition. MF-MAPPO employs a shared actor and a minimally informed critic per team and is trained directly on finite-population simulators, thereby enabling deployment to realistic scenarios with thousands of agents. We further show that MF-MAPPO naturally extends to partially observable settings through a simple gradient-regularized training scheme. Our evaluation utilizes large-scale benchmark scenarios using our own testing simulation platform for MF team games (MFEnv), including offense-defense battlefield tasks as well as variants of population-based rock-paper-scissors games that admit analytical solutions, for benchmarking. Across these benchmarks, MF-MAPPO outperforms existing methods and exhibits complex, heterogeneous behaviors, demonstrating the effectiveness of combining mean-field theory and MARL techniques at scale.