# Model Predictive Mean Field Games for Controlling Multi-Agent Systems

arXiv: https://arxiv.org/abs/2004.07994 · HTML: https://mlsanity.com/paper/2004.07994/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Apr 2020.

## Built on by (most cited first, 2 of 2)

- [Bounded Rationality Equilibrium Learning in Mean Field Games](https://mlsanity.com/paper/2411.07099/) (2024)
- [Recurrent Structural Policy Gradient for Partially Observable Mean Field Games](https://mlsanity.com/paper/2602.20141/) (2026)

## Abstract (arXiv)

When controlling multi-agent systems, the trade-off between performance and scalability is a major challenge. Here, we address this difficulty by using mean field games (MFGs), which is a framework that deduces the macroscopic dynamics describing the density profile of agents from their microscopic dynamics. To effectively use the MFG, we propose a model predictive MFG (MP-MFG), which estimates the agent population density profile with using kernel density estimation and manages the input generation with model predictive control. The proposed MP-MFG generates control inputs by monitoring the agent population at each time step, and thus achieves higher robustness than the conventional MFG. Numerical results show that the MP-MFG outperforms the MFG when the agent model has modeling errors or the number of agents in the system is small.