# A mean-field game model for homogeneous flocking

arXiv: https://arxiv.org/abs/1803.05250 · HTML: https://mlsanity.com/paper/1803.05250/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Mar 2018.

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

- [Cooperation and Competition: Flocking with Evolutionary Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2209.04696/) (2022)
- [A Schr"odinger Eigenfunction Method for Long-Horizon Stochastic Optimal Control](https://mlsanity.com/paper/2603.23173/) (2026)

## Abstract (arXiv)

Empirically derived continuum models of collective behavior among large populations of dynamic agents are a subject of intense study in several fields, including biology, engineering and finance. We formulate and study a mean-field game model whose behavior mimics an empirically derived non-local homogeneous flocking model for agents with gradient self-propulsion dynamics. The mean-field game framework provides a non-cooperative optimal control description of the behavior of a population of agents in a distributed setting. In this description, each agent's state is driven by optimally controlled dynamics that result in a Nash equilibrium between itself and the population. The optimal control is computed by minimizing a cost that depends only on its own state, and a mean-field term. The agent distribution in phase space evolves under the optimal feedback control policy. We exploit the low-rank perturbative nature of the non-local term in the forward-backward system of equations governing the state and control distributions, and provide a linear stability analysis demonstrating that our model exhibits bifurcations similar to those found in the empirical model. The present work is a step towards developing a set of tools for systematic analysis, and eventually design, of collective behavior of non-cooperative dynamic agents via an inverse modeling approach.