# Reinforcement Learning for Mean Field Game

arXiv: https://arxiv.org/abs/1905.13357 · HTML: https://mlsanity.com/paper/1905.13357/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 May 2019.

## Built on by (most cited first, 5 of 5)

- [Efficient Model-Based Multi-Agent Mean-Field Reinforcement Learning](https://mlsanity.com/paper/2107.04050/) (2021)
- [On the Approximation of Cooperative Heterogeneous Multi-Agent Reinforcement Learning (MARL) using Mean Field Control (MFC)](https://mlsanity.com/paper/2109.04024/) (2021)
- [Signatured Deep Fictitious Play for Mean Field Games with Common Noise](https://mlsanity.com/paper/2106.03272/) (2021)
- [On the Near-Optimality of Local Policies in Large Cooperative Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2209.03491/) (2022)
- [From Individual Learning to Market Equilibrium: Correcting Structural and Parametric Biases in RL Simulations of Economic Models](https://mlsanity.com/paper/2507.18229/) (2025)

## Abstract (arXiv)

Stochastic games provide a framework for interactions among multiple agents and enable a myriad of applications. In these games, agents decide on actions simultaneously, the state of every agent moves to the next state, and each agent receives a reward. However, finding an equilibrium (if exists) in this game is often difficult when the number of agents becomes large. This paper focuses on finding a mean-field equilibrium (MFE) in an action coupled stochastic game setting in an episodic framework. It is assumed that the impact of the other agents' can be assumed by the empirical distribution of the mean of the actions. All agents know the action distribution and employ lower-myopic best response dynamics to choose the optimal oblivious strategy. This paper proposes a posterior sampling based approach for reinforcement learning in the mean-field game, where each agent samples a transition probability from the previous transitions. We show that the policy and action distributions converge to the optimal oblivious strategy and the limiting distribution, respectively, which constitute an MFE.