# Mean Field Games for Multi-agent Systems with Multiplicative Noises

arXiv: https://arxiv.org/abs/1906.03177 · HTML: https://mlsanity.com/paper/1906.03177/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Jun 2019.

## Built on by (most cited first, 1 of 1)

- [Mean Field LQG Social Optimization: A Reinforcement Learning Approach](https://mlsanity.com/paper/2410.15119/) (2024)

## Abstract (arXiv)

This paper studies mean field games for multi-agent systems with control-dependent multiplicative noises. For the general systems with nonuniform agents, we obtain a set of decentralized strategies by solving an auxiliary limiting optimal control problem subject to consistent mean field approximations. The set of decentralized strategies is further shown to be an varepsilon-Nash equilibrium. For the integrator multiagent systems, we design a set of varepsilon-Nash strategies by exploiting the convexity property of the limiting problem. It is shown that under the mild conditions all the agents achieve mean-square consensus.