Robust Mean-Field Games with Risk Aversion and Bounded Rationality

TL;DR

This paper introduces a new equilibrium concept called the mean-field risk-averse quantal response equilibrium (MF-RQE) that accounts for distributional uncertainty and bounded rationality in large-scale multi-agent systems, with proven existence, convergence, and scalable learning algorithms.

Contribution

It extends classical mean-field game models by incorporating risk aversion and bounded rationality, providing a more robust and general framework with theoretical guarantees and practical algorithms.

Findings

MF-RQE policies improve robustness over classical approaches.

Proven existence and convergence of fixed-point and learning algorithms.

Numerical experiments validate the effectiveness of the proposed methods.

Abstract

Recent advances in mean-field game literature enable the reduction of large-scale multi-agent problems to tractable interactions between a representative agent and a population distribution. However, existing approaches typically assume a fixed initial population distribution and fully rational agents, limiting robustness under distributional uncertainty and cognitive constraints. We address these limitations by introducing risk aversion with respect to the initial population distribution and by incorporating bounded rationality to model deviations from fully rational decision-making agents. The combination of these two elements yields a new and more general equilibrium concept, which we term the mean-field risk-averse quantal response equilibrium (MF-RQE). We establish existence results and prove convergence of fixed-point iteration and fictitious play to MF-RQE. Building on these insights, we develop a scalable reinforcement learning algorithm for scenarios with large state-action spaces. Numerical experiments demonstrate that MF-RQE policies achieve improved robustness relative to classical mean-field approaches that optimize expected cumulative rewards under a fixed initial distribution and are restricted to entropy-based regularizers.