Risk-Averse Multi-Population Mean-Field Games

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 $\mathcal{O}(1/s)$, 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.