# Learning in Mean Field Games: the Fictitious Play

arXiv: https://arxiv.org/abs/1507.06280 · HTML: https://mlsanity.com/paper/1507.06280/

## Key facts

- Cited by 38 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Jul 2015.

## Built on by (most cited first, 30 of 38)

- [Approximately Solving Mean Field Games via Entropy-Regularized Deep Reinforcement Learning](https://mlsanity.com/paper/2102.01585/) (2021)
- [Concave Utility Reinforcement Learning: the Mean-Field Game Viewpoint](https://mlsanity.com/paper/2106.03787/) (2021)
- [Efficient Model-Based Multi-Agent Mean-Field Reinforcement Learning](https://mlsanity.com/paper/2107.04050/) (2021)
- [Scalable Deep Reinforcement Learning Algorithms for Mean Field Games](https://mlsanity.com/paper/2203.11973/) (2022)
- [Scaling up Mean Field Games with Online Mirror Descent](https://mlsanity.com/paper/2103.00623/) (2021)
- [Mean Field Games Flock! The Reinforcement Learning Way](https://mlsanity.com/paper/2105.07933/) (2021)
- [Generalization in Mean Field Games by Learning Master Policies](https://mlsanity.com/paper/2109.09717/) (2021)
- [Learning Graphon Mean Field Games and Approximate Nash Equilibria](https://mlsanity.com/paper/2112.01280/) (2021)
- [Reinforcement Learning for Mean Field Games, with Applications to Economics](https://mlsanity.com/paper/2106.13755/) (2021)
- [A Survey on Large-Population Systems and Scalable Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2209.03859/) (2022)
- [Learning Sparse Graphon Mean Field Games](https://mlsanity.com/paper/2209.03880/) (2022)
- [Signatured Deep Fictitious Play for Mean Field Games with Common Noise](https://mlsanity.com/paper/2106.03272/) (2021)
- [Adversarial Inverse Reinforcement Learning for Mean Field Games](https://mlsanity.com/paper/2104.14654/) (2021)
- [Learning Correlated Equilibria in Mean-Field Games](https://mlsanity.com/paper/2208.10138/) (2022)
- [Regularization of the policy updates for stabilizing Mean Field Games](https://mlsanity.com/paper/2304.01547/) (2023)
- [Population-aware Online Mirror Descent for Mean-Field Games by Deep Reinforcement Learning](https://mlsanity.com/paper/2403.03552/) (2024)
- [Graphon Mean Field Games with a Representative Player: Analysis and Learning Algorithm](https://mlsanity.com/paper/2405.08005/) (2024)
- [Stochastic Semi-Gradient Descent for Learning Mean Field Games with Population-Aware Function Approximation](https://mlsanity.com/paper/2408.08192/) (2024)
- [Primal and Dual Analysis of Entropic Fictitious Play for Finite-sum Problems](https://mlsanity.com/paper/2303.02957/) (2023)
- [Population-aware Online Mirror Descent for Mean-Field Games with Common Noise by Deep Reinforcement Learning](https://mlsanity.com/paper/2509.03030/) (2025)
- [Exploration noise for learning linear-quadratic mean field games](https://mlsanity.com/paper/2107.00839/) (2021)
- [Hypergraphon Mean Field Games](https://mlsanity.com/paper/2203.16223/) (2022)
- [Learning Mean Field Games on Sparse Graphs: A Hybrid Graphex Approach](https://mlsanity.com/paper/2401.12686/) (2024)
- [Meta-Inverse Reinforcement Learning for Mean Field Games via Probabilistic Context Variables](https://mlsanity.com/paper/2509.03845/) (2025)
- [High-dimensional Mean-Field Games by Particle-based Flow Matching](https://mlsanity.com/paper/2512.01172/) (2025)
- [A Single Online Agent Can Efficiently Learn Mean Field Games](https://mlsanity.com/paper/2405.03718/) (2024)
- [Solving Continuous Mean Field Games: Deep Reinforcement Learning for Non-Stationary Dynamics](https://mlsanity.com/paper/2510.22158/) (2025)
- [Scalable Offline Reinforcement Learning for Mean Field Games](https://mlsanity.com/paper/2410.17898/) (2024)
- [Bench-MFG: A Benchmark Suite for Learning in Stationary Mean Field Games](https://mlsanity.com/paper/2602.12517/) (2026)
- [Mean Field Equilibrium in Multi-Armed Bandit Game with Continuous Reward](https://mlsanity.com/paper/2105.00767/) (2021)

## Abstract (arXiv)

Mean Field Game systems describe equilibrium configurations in differential games with infinitely many infinitesimal interacting agents. We introduce a learning procedure (similar to the Fictitious Play) for these games and show its convergence when the Mean Field Game is potential.