arXiv：cs.LG· Bhavini Jeloka, Siddhartha Ganguly, Panagiotis Tsiotras·· 4 小时前AI 评分27
风险规避多群体平均场博弈：超越名义均衡
Beyond Nominal Equilibria: Risk-Averse Multi-Population Mean-Field Games
AI 导读
研究提出风险规避多群体平均场博弈新范式，每个群体在其余部分群体平均场流的动态可行模糊集上优化最坏情况期望收益。作者利用占用测度表述与集值分析工具，证明了模糊集几何性质及新型风险规避多群体平均场均衡的存在性，并在熵正则化下给出不动点算子的收缩性结果，可用于学习均衡。进一步提出风险规避虚拟博弈方案，显示可利用度收敛至零，数值实验验证了收敛性与风险规避行为。
正文
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.
| Comments: | Submitted to a conference; comments are welcome |
| Subjects: | Optimization and Control (math.OC); Computer Science and Game Theory (cs.GT); Machine Learning (cs.LG); Systems and Control (eess.SY) |
| MSC classes: | 91A13, 91A15, 49J53 |
| Cite as: | arXiv:2610.09244 [math.OC] |
| (or arXiv:2610.09244v1 [math.OC] for this version) | |
| https://doi.org/10.48550/arXiv.2610.09244 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Siddhartha Ganguly [view email]
[v1]
Wed, 7 Oct 2026 00:15:13 UTC (1,493 KB)
来源：arXiv：cs.LG · arxiv.org