mlsanityData to 7 Oct 2026

Graphon Mean Field Games with a Representative Player: Analysis and Learning Algorithm

arXiv 2405.08005 ↗First posted 8 May 2024math.OC cs.AI cs.GTcited by 5

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Abstract (arXiv)

We propose a discrete time graphon game formulation on continuous state and action spaces using a representative player to study stochastic games with heterogeneous interaction among agents. This formulation admits both philosophical and mathematical advantages, compared to a widely adopted formulation using a continuum of players. We prove the existence and uniqueness of the graphon equilibrium with mild assumptions, and show that this equilibrium can be used to construct an approximate solution for finite player game on networks, which is challenging to analyze and solve due to curse of dimensionality. An online oracle-free learning algorithm is developed to solve the equilibrium numerically, and sample complexity analysis is provided for its convergence.

Key facts. Cited by 5 papers in the map (data through 7 Oct 2026). Builds on 23 of its 52 references that are in the map. First posted on arXiv 8 May 2024.

Builds on

23 of 52 references.

References · 23

  1. 2018Mean Field Multi-Agent Reinforcement Learningcited by 202
  2. 2017On the Properties of the Softmax Function with Application in Game Theory and Reinforcement Learningcited by 136
  3. 2019Finite-Sample Analysis for SARSA with Linear Function Approximationcited by 85
  4. 2021Approximately Solving Mean Field Games via Entropy-Regularized Deep Reinforcement Learningcited by 65
  5. 2020Fictitious Play for Mean Field Games: Continuous Time Analysis and Applicationscited by 57
  6. 2019On the Convergence of Model Free Learning in Mean Field Gamescited by 45
  7. 2020Unified Reinforcement Q-Learning for Mean Field Game and Control Problemscited by 42
  8. 2015Learning in Mean Field Games: the Fictitious Playcited by 37
  9. 2022Scalable Deep Reinforcement Learning Algorithms for Mean Field Gamescited by 33
  10. 2021Mean Field Games Flock! The Reinforcement Learning Waycited by 30
  11. 2021Generalization in Mean Field Games by Learning Master Policiescited by 28
  12. 2021Learning Graphon Mean Field Games and Approximate Nash Equilibriacited by 28
11 more
  1. 2020Breaking the Curse of Many Agents: Provable Mean Embedding Q-Iteration for Mean-Field Reinforcement Learningcited by 19
  2. 2022Learning Sparse Graphon Mean Field Gamescited by 14
  3. 2019Stochastic Graphon Games: I. The Static Casecited by 12
  4. 2020Graphon Mean Field Games and the GMFG Equationscited by 11
  5. 2019A Game-Theoretic Framework for Autonomous Vehicles Velocity Control: Bridging Microscopic Differential Games and Macroscopic Mean Field Gamescited by 9
  6. 2017Learning Deep Mean Field Games for Modeling Large Population Behaviorcited by 8
  7. 2023Learning Regularized Monotone Graphon Mean-Field Gamescited by 8
  8. 2020Linear Quadratic Graphon Field Gamescited by 5
  9. 2022A label-state formulation of stochastic graphon games and approximate equilibria on large networkscited by 4
  10. 2014Mean field games via controlled martingale problems: Existence of Markovian equilibriacited by 2
  11. 2024A Single Online Agent Can Efficiently Learn Mean Field Gamescited by 2

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 1; 2025: 2; 2026: 2.

5 papers.

  1. 2024Stochastic Semi-Gradient Descent for Learning Mean Field Games with Population-Aware Function Approximationcited by 5
  2. 2025Learning Mean Field Control on Sparse Graphscited by 2
  3. 2025Policy Optimization for Continuous-time Linear-Quadratic Graphon Mean Field Gamescited by 1
  4. 2026Mean-Field Reinforcement Learning without Synchronycited by 1
  5. 2026All in One: Generative Modeling as Mean-Field Game Designcited by 0