Problem
Research questions and friction points this paper is trying to address.
multi-population mean-field games
risk-averse
uncertainty
ambiguity sets
mean-field equilibrium
Beyond Nominal Equilibria: Risk-Averse Multi-Population Mean-Field Games
🤖 AI Summary
This study addresses the limitation of existing multi-population games that neglect behavioral uncertainty by introducing a risk-averse multi-population mean field game framework, which enhances system robustness through optimizing worst-case expected rewards. Methodologically, the proposed paradigm integrates occupancy measure formulations, set-valued analysis, and entropy regularization techniques. The existence of equilibrium is rigorously established, and contractivity results are derived. Furthermore, a fictitious play-based algorithm is developed to solve the formulated problem, with theoretical guarantees demonstrating that exploitability converges to zero. Numerical experiments validate the effectiveness of the proposed approach.
📝 Abstract
Recent advances in mean-field games and its multi-population variants enable large-scale heterogeneous multi-agent systems to be modeled through representative agents and their associated mean-field distributions. However, existing approaches do not explicitly account for uncertainty in the behavior of other populations. To this end, we introduce a new paradigm: risk-averse multi-population mean-field games, where each population optimizes a worst-case expected reward over dynamically feasible ambiguity sets of mean-field flows of a subset of the other populations. Employing an occupation-measure formulation along with tools from set-valued analysis, we establish, under mild assumptions, several theoretical properties of the multi-population game, including the geometric properties of the ambiguity sets and the existence of a novel risk-averse multi-population mean-field equilibrium. Further, we derive contractivity results of the fixed-point operator under entropy regularization and show that it can be utilized to learn the equilibrium. Finally, we propose a risk-averse fictitious-play scheme and show that exploitability decays to zero, despite the additional nonlinearity introduced by the worst-case objective. We report several numerical experiments to illustrate convergence and risk-averse behavior.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Risk-Averse Multi-Population Mean-Field Games
Ambiguity Sets
Occupation-Measure Formulation
Entropy Regularization
Fictitious Play
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