mlsanityData to 7 Oct 2026

Fictitious Play for Mean Field Games: Continuous Time Analysis and Applications

arXiv 2007.03458 ↗First posted 5 Jul 2020math.OC cs.AIcited by 57

Not on the map. Why?

Abstract (arXiv)

In this paper, we deepen the analysis of continuous time Fictitious Play learning algorithm to the consideration of various finite state Mean Field Game settings (finite horizon, γ-discounted), allowing in particular for the introduction of an additional common noise. We first present a theoretical convergence analysis of the continuous time Fictitious Play process and prove that the induced exploitability decreases at a rate O(frac1t). Such analysis emphasizes the use of exploitability as a relevant metric for evaluating the convergence towards a Nash equilibrium in the context of Mean Field Games. These theoretical contributions are supported by numerical experiments provided in either model-based or model-free settings. We provide hereby for the first time converging learning dynamics for Mean Field Games in the presence of common noise.

Key facts. Cited by 57 papers in the map (data through 7 Oct 2026). First posted on arXiv 5 Jul 2020.

Builds on

No reference list yet.

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 8; 2022: 7; 2023: 13; 2024: 15; 2025: 6; 2026: 8.

57 papers.

Sort:

By area:

  1. 2021Approximately Solving Mean Field Games via Entropy-Regularized Deep Reinforcement Learningcited by 65
  2. 2021Concave Utility Reinforcement Learning: the Mean-Field Game Viewpointcited by 54
  3. 2022Scalable Deep Reinforcement Learning Algorithms for Mean Field Gamescited by 33
  4. 2021Mean Field Games Flock! The Reinforcement Learning Waycited by 30
  5. 2021Scaling up Mean Field Games with Online Mirror Descentcited by 29
  6. 2021Generalization in Mean Field Games by Learning Master Policiescited by 28
  7. 2022Policy Mirror Ascent for Efficient and Independent Learning in Mean Field Gamescited by 24
  8. 2021Reinforcement Learning for Mean Field Games, with Applications to Economicscited by 14
  9. 2022Learning Sparse Graphon Mean Field Gamescited by 14
  10. 2023On the Statistical Efficiency of Mean-Field Reinforcement Learning with General Function Approximationcited by 13
  11. 2021Signatured Deep Fictitious Play for Mean Field Games with Common Noisecited by 12
  12. 2022A Survey on Large-Population Systems and Scalable Multi-Agent Reinforcement Learningcited by 12
38 more
  1. 2023On Imitation in Mean-field Gamescited by 10
  2. 2024Model-Based RL for Mean-Field Games is not Statistically Harder than Single-Agent RLcited by 9
  3. 2023Multi-Player Zero-Sum Markov Games with Networked Separable Interactionscited by 8
  4. 2023Learning Regularized Monotone Graphon Mean-Field Gamescited by 8
  5. 2024Unified continuous-time q-learning for mean-field game and mean-field control problemscited by 7
  6. 2023Learning Decentralized Partially Observable Mean Field Control for Artificial Collective Behaviorcited by 6
  7. 2023Regularization of the policy updates for stabilizing Mean Field Gamescited by 5
  8. 2024Population-aware Online Mirror Descent for Mean-Field Games by Deep Reinforcement Learningcited by 5
  9. 2024MF-OML: Online Mean-Field Reinforcement Learning with Occupation Measures for Large Population Gamescited by 5
  10. 2024Graphon Mean Field Games with a Representative Player: Analysis and Learning Algorithmcited by 5
  11. 2024Stochastic Semi-Gradient Descent for Learning Mean Field Games with Population-Aware Function Approximationcited by 5
  12. 2022Learning Correlated Equilibria in Mean-Field Gamescited by 4
  13. 2023Primal and Dual Analysis of Entropic Fictitious Play for Finite-sum Problemscited by 4
  14. 2023Major-Minor Mean Field Multi-Agent Reinforcement Learningcited by 4
  15. 2025Population-aware Online Mirror Descent for Mean-Field Games with Common Noise by Deep Reinforcement Learningcited by 4
  16. 2021Exploration noise for learning linear-quadratic mean field gamescited by 3
  17. 2022Mean Field Games on Weighted and Directed Graphs via Colored Digraphonscited by 3
  18. 2023Population-size-Aware Policy Optimization for Mean-Field Gamescited by 3
  19. 2024Learning Mean Field Games on Sparse Graphs: A Hybrid Graphex Approachcited by 3
  20. 2025Convergence of Actor-Critic Learning for Mean Field Games and Mean Field Control in Continuous Spacescited by 3
  21. 2025High-dimensional Mean-Field Games by Particle-based Flow Matchingcited by 3
  22. 2022Developing, Evaluating and Scaling Learning Agents in Multi-Agent Environmentscited by 2
  23. 2023Learning Discrete-Time Major-Minor Mean Field Gamescited by 2
  24. 2024A Single Online Agent Can Efficiently Learn Mean Field Gamescited by 2
  25. 2024Exploiting Approximate Symmetry for Efficient Multi-Agent Reinforcement Learningcited by 2
  26. 2025Finite-Sample Convergence Bounds for Trust Region Policy Optimization in Mean-Field Gamescited by 2
  27. 2025Solving Continuous Mean Field Games: Deep Reinforcement Learning for Non-Stationary Dynamicscited by 2
  28. 2023MESOB: Balancing Equilibria & Social Optimalitycited by 1
  29. 2024Reinforcement Learning for Finite Space Mean-Field Type Gamescited by 1
  30. 2024Scalable Offline Reinforcement Learning for Mean Field Gamescited by 1
  31. 2025Convergence and Connectivity: Dynamics of Multi-Agent Q-Learning in Random Networkscited by 1
  32. 2026Bench-MFG: A Benchmark Suite for Learning in Stationary Mean Field Gamescited by 1
  33. 2026Mean-Field Reinforcement Learning without Synchronycited by 1
  34. 2023Reimagining Demand-Side Management with Mean Field Learningcited by 0
  35. 2023Networked Communication for Decentralised Agents in Mean-Field Gamescited by 0
  36. 2024Mean Field Correlated Imitation Learningcited by 0
  37. 2024Networked Communication for Mean-Field Games with Function Approximation and Empirical Mean-Field Estimationcited by 0
  38. 2024Last Iterate Convergence in Monotone Mean Field Gamescited by 0

50 most cited of 57 All 57 (JSON)