# A Machine Learning Method for Stackelberg Mean Field Games

arXiv: https://arxiv.org/abs/2302.10440 · HTML: https://mlsanity.com/paper/2302.10440/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Feb 2023.

## Built on by (most cited first, 4 of 4)

- [Neural Operators Can Play Dynamic Stackelberg Games](https://mlsanity.com/paper/2411.09644/) (2024)
- [Learning in Stackelberg Mean Field Games: A Non-Asymptotic Analysis](https://mlsanity.com/paper/2509.15392/) (2025)
- [A Deep Learning Method for Optimal Investment Under Relative Performance Criteria Among Heterogeneous Agents](https://mlsanity.com/paper/2402.07365/) (2024)
- [DeepPAAC: A New Deep Galerkin Method for Principal-Agent Problems](https://mlsanity.com/paper/2511.04309/) (2025)

## Abstract (arXiv)

We propose a single-level numerical approach to solve Stackelberg mean field game (MFG) problems. In Stackelberg MFG, an infinite population of agents play a non-cooperative game and choose their controls to optimize their individual objectives while interacting with the principal and other agents through the population distribution. The principal can influence the mean field Nash equilibrium at the population level through policies, and she optimizes her own objective, which depends on the population distribution. This leads to a bi-level problem between the principal and mean field of agents that cannot be solved using traditional methods for MFGs. We propose a reformulation of this problem as a single-level mean field optimal control problem through a penalization approach. We prove convergence of the reformulated problem to the original problem. We propose a machine learning method based on (feed-forward and recurrent) neural networks and illustrate it on several examples from the literature.