# Learning Discrete-Time Major-Minor Mean Field Games

arXiv: https://arxiv.org/abs/2312.10787 · HTML: https://mlsanity.com/paper/2312.10787/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 42 references that are in the map.
- First posted on arXiv 17 Dec 2023.

## Builds on (most cited first, 14 of 14)

- [Game-Theoretic Multiagent Reinforcement Learning](https://mlsanity.com/paper/2011.00583/) (2020)
- [Approximately Solving Mean Field Games via Entropy-Regularized Deep Reinforcement Learning](https://mlsanity.com/paper/2102.01585/) (2021)
- [Fictitious Play for Mean Field Games: Continuous Time Analysis and Applications](https://mlsanity.com/paper/2007.03458/) (2020)
- [Entropy Regularization for Mean Field Games with Learning](https://mlsanity.com/paper/2010.00145/) (2020)
- [Mean-Field Controls with Q-learning for Cooperative MARL: Convergence and Complexity Analysis](https://mlsanity.com/paper/2002.04131/) (2020)
- [Efficient Model-Based Multi-Agent Mean-Field Reinforcement Learning](https://mlsanity.com/paper/2107.04050/) (2021)
- [Markov-Nash Equilibria in Mean-Field Games with Discounted Cost](https://mlsanity.com/paper/1612.07878/) (2016)
- [Mean-field Markov decision processes with common noise and open-loop controls](https://mlsanity.com/paper/1912.07883/) (2019)
- [Mean-Field-Type Games in Engineering](https://mlsanity.com/paper/1605.03281/) (2016)
- [A tale of a Principal and many many Agents](https://mlsanity.com/paper/1608.05226/) (2016)
- [Mean Field Models to Regulate Carbon Emissions in Electricity Production](https://mlsanity.com/paper/2102.09434/) (2021)
- [Master Equation for Discrete-Time Stackelberg Mean Field Games with single leader](https://mlsanity.com/paper/2201.05959/) (2022)
- [Mean Field Games with a Dominating Player](https://mlsanity.com/paper/1404.4148/) (2014)
- [Remarks on Nash equilibria in mean field game models with a major player](https://mlsanity.com/paper/1811.02811/) (2018)

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

- [Learning in Stackelberg Mean Field Games: A Non-Asymptotic Analysis](https://mlsanity.com/paper/2509.15392/) (2025)
- [Fair Policy Optimization in Major-Minor Weakly Coupled Markov Decision Processes](https://mlsanity.com/paper/2609.36174/) (2026)

## Abstract (arXiv)

Recent techniques based on Mean Field Games (MFGs) allow the scalable analysis of multi-player games with many similar, rational agents. However, standard MFGs remain limited to homogeneous players that weakly influence each other, and cannot model major players that strongly influence other players, severely limiting the class of problems that can be handled. We propose a novel discrete time version of major-minor MFGs (M3FGs), along with a learning algorithm based on fictitious play and partitioning the probability simplex. Importantly, M3FGs generalize MFGs with common noise and can handle not only random exogeneous environment states but also major players. A key challenge is that the mean field is stochastic and not deterministic as in standard MFGs. Our theoretical investigation verifies both the M3FG model and its algorithmic solution, showing firstly the well-posedness of the M3FG model starting from a finite game of interest, and secondly convergence and approximation guarantees of the fictitious play algorithm. Then, we empirically verify the obtained theoretical results, ablating some of the theoretical assumptions made, and show successful equilibrium learning in three example problems. Overall, we establish a learning framework for a novel and broad class of tractable games.