Recent advances in multi-population mean-field games (MP-MFGs) typically rely on expected-value objectives and do not account for uncertainty in the behavior of other populations. We introduce risk-averse MP-MFGs, a framework in which each population optimizes its worst-case expected reward over dynamically feasible ambiguity sets centered on the other team's nominal mean-field flows. We develop a risk-averse fictitious-play algorithm and show, under mild monotonicity and regularity conditions, that risk-averse exploitability serves as a Lyapunov function and decays at a rate O(1/s), despite the additional nonlinearity introduced by the worst-case objective. Numerical experiments demonstrate convergence and illustrate the resulting risk-averse behaviors in multi-population decision-making.
While MARL has shown strong empirical performance, existing methods struggle with a large number of agents due to the combinatorial growth of joint interactions. Mean-field (MF) approximations address this challenge by replacing pairwise interactions with surrogate interactions against population distributions, yielding tractable formulations for solving large-population policies. However, existing MF formulations focus on fully cooperative or purely competitive settings and fail to capture the mixed cooperativeβcompetitive structure of team-based games. We extend mean-field learning to zero-sum team games, where agents cooperate within each team and compete at the team level. We show that such games admit ε-optimal decentralized policies that depend only on each agent's local state and population team distributions. Building on this structure, we propose MF-MAPPO, a scalable algorithm with a shared actor and a minimally informed critic per team. MF-MAPPO is trained directly in finite-population simulators rather than using mean-field oracles, enabling deployment to realistic scenarios with thousands of agents. We further extend MF-MAPPO to partially observable settings via a simple gradient-regularized training scheme. Experiments on large-scale benchmarks in our simulation platform (MFEnv), including population games with analytical solutions and high-dimensional battlefield scenarios, demonstrate that MF-MAPPO outperforms existing MARL baselines and yields rich, heterogeneous behaviors.
Mean-field games address scalability in large-population multi-agent systems by reducing inter-agent interactions to those between a representative agent and an aggregate population distribution. However, standard mean-field problem formulations assume either fully rational agents and/or a fixed and known initial agent distribution. To address these limitations, we introduce a unified framework that incorporates risk aversion to uncertainty in the initial population distribution together with an explicit quantal-response model of bounded rationality, leading to a generalized equilibrium concept, which we call the mean-field risk-averse quantal response equilibrium (MF-RQE). We prove the existence of MF-RQE, establish convergence guarantees for fixed-point iteration and fictitious play, and propose a scalable reinforcement learning algorithm for large stateβaction spaces. Numerical experiments show that MF-RQE yields superior robustness over classical MFG baselines under distributional shifts and agent suboptimality.