# Reinforcement Learning Algorithm for Mixed Mean Field Control Games

arXiv: https://arxiv.org/abs/2205.02330 · HTML: https://mlsanity.com/paper/2205.02330/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 May 2022.

## Built on by (most cited first, 7 of 7)

- [Deep Reinforcement Learning for Infinite Horizon Mean Field Problems in Continuous Spaces](https://mlsanity.com/paper/2309.10953/) (2023)
- [Stochastic Semi-Gradient Descent for Learning Mean Field Games with Population-Aware Function Approximation](https://mlsanity.com/paper/2408.08192/) (2024)
- [Markov Decision Processes under Model Uncertainty](https://mlsanity.com/paper/2206.06109/) (2022)
- [Analysis of Multiscale Reinforcement Q-Learning Algorithms for Mean Field Control Games](https://mlsanity.com/paper/2405.17017/) (2024)
- [Convergence of Actor-Critic Learning for Mean Field Games and Mean Field Control in Continuous Spaces](https://mlsanity.com/paper/2511.06812/) (2025)
- [Q-Learning under Finite Model Uncertainty](https://mlsanity.com/paper/2407.04259/) (2024)
- [Reinforcement Learning for Finite Space Mean-Field Type Games](https://mlsanity.com/paper/2409.18152/) (2024)

## Abstract (arXiv)

We present a new combined textitmean field control game (MFCG) problem which can be interpreted as a competitive game between collaborating groups and its solution as a Nash equilibrium between groups. Players coordinate their strategies within each group. An example is a modification of the classical trader's problem. Groups of traders maximize their wealth. They face cost for their transactions, for their own terminal positions, and for the average holding within their group. The asset price is impacted by the trades of all agents. We propose a three-timescale reinforcement learning algorithm to approximate the solution of such MFCG problems. We test the algorithm on benchmark linear-quadratic specifications for which we provide analytic solutions.