mlsanityData to 14 Oct 2026

Markov-Nash Equilibria in Mean-Field Games with Discounted Cost

arXiv 1612.07878 ↗First posted 23 Dec 2016eess.SY cs.SY math.OCcited by 31

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Abstract (arXiv)

In this paper, we consider discrete-time dynamic games of the mean-field type with a finite number N of agents subject to an infinite-horizon discounted-cost optimality criterion. The state space of each agent is a locally compact Polish space. At each time, the agents are coupled through the empirical distribution of their states, which affects both the agents' individual costs and their state transition probabilities. We introduce a new solution concept of the Markov-Nash equilibrium, under which a policy is player-by-player optimal in the class of all Markov policies. Under mild assumptions, we demonstrate the existence of a mean-field equilibrium in the infinite-population limit N → ∞, and then show that the policy obtained from the mean-field equilibrium is approximately Markov-Nash when the number of agents N is sufficiently large.

Key facts. Cited by 31 papers in the map (data through 14 Oct 2026). First posted on arXiv 23 Dec 2016.

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Citing papers per year: 2021: 4; 2022: 8; 2023: 6; 2024: 8; 2025: 0; 2026: 5.

31 papers.

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  1. 2021Approximately Solving Mean Field Games via Entropy-Regularized Deep Reinforcement Learningcited by 73
  2. 2021Learning Graphon Mean Field Games and Approximate Nash Equilibriacited by 28
  3. 2022Policy Mirror Ascent for Efficient and Independent Learning in Mean Field Gamescited by 26
  4. 2022Oracle-free Reinforcement Learning in Mean-Field Games along a Single Sample Pathcited by 20
  5. 2022A Survey on Large-Population Systems and Scalable Multi-Agent Reinforcement Learningcited by 14
  6. 2022Learning Sparse Graphon Mean Field Gamescited by 14
  7. 2023On the Statistical Efficiency of Mean-Field Reinforcement Learning with General Function Approximationcited by 14
  8. 2024Unified continuous-time q-learning for mean-field game and mean-field control problemscited by 13
  9. 2022Individual-Level Inverse Reinforcement Learning for Mean Field Gamescited by 10
  10. 2021Adversarial Inverse Reinforcement Learning for Mean Field Gamescited by 8
  11. 2024When is Mean-Field Reinforcement Learning Tractable and Relevant?cited by 8
  12. 2021Discrete-Time Mean Field Control with Environment Statescited by 7
19 more
  1. 2024MF-OML: Online Mean-Field Reinforcement Learning with Occupation Measures for Large Population Gamescited by 5
  2. 2023Major-Minor Mean Field Multi-Agent Reinforcement Learningcited by 4
  3. 2022Hypergraphon Mean Field Gamescited by 3
  4. 2022Mean Field Games on Weighted and Directed Graphs via Colored Digraphonscited by 3
  5. 2023Population-size-Aware Policy Optimization for Mean-Field Gamescited by 3
  6. 2022Learning Mean-Field Control for Delayed Information Load Balancing in Large Queuing Systemscited by 2
  7. 2023Learning Discrete-Time Major-Minor Mean Field Gamescited by 2
  8. 2024Exploiting Approximate Symmetry for Efficient Multi-Agent Reinforcement Learningcited by 2
  9. 2024Reinforcement Learning for Finite Space Mean-Field Type Gamescited by 2
  10. 2023MESOB: Balancing Equilibria & Social Optimalitycited by 1
  11. 2026Mean-Field Reinforcement Learning without Synchronycited by 1
  12. 2023Networked Communication for Decentralised Agents in Mean-Field Gamescited by 0
  13. 2024Networked Communication for Mean-Field Games with Function Approximation and Empirical Mean-Field Estimationcited by 0
  14. 2024Last Iterate Convergence in Monotone Mean Field Gamescited by 0
  15. 2024Bounded Rationality Equilibrium Learning in Mean Field Gamescited by 0
  16. 2026Mean-Field Control on Sparse Graphs: From Local Limits to GNNs via Neighborhood Distributionscited by 0
  17. 2026Stationary Robust Mean-Field Games under Model Mismatchescited by 0
  18. 2026Towards Scaling Reinforcement Learning to Massive Populations: Learning Mean-Field Representationscited by 0
  19. 2026Entropy-Regularized Mean-Field Games with Average-Reward Criterion: Span-Seminorm Contractions and Model-Free Learningcited by 0