mlsanityData to 14 Oct 2026

Mean Field Game of Controls and An Application To Trade Crowding

arXiv 1610.09904 ↗First posted 31 Oct 2016q-fin.TR math.OCcited by 23

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Abstract (arXiv)

In this paper we formulate the now classical problem of optimal liquidation (or optimal trading) inside a Mean Field Game (MFG). This is a noticeable change since usually mathematical frameworks focus on one large trader in front of a "background noise" (or "mean field"). In standard frameworks, the interactions between the large trader and the price are a temporary and a permanent market impact terms, the latter influencing the public price. In this paper the trader faces the uncertainty of fair price changes too but not only. He has to deal with price changes generated by other similar market participants, impacting the prices permanently too, and acting strategically. Our MFG formulation of this problem belongs to the class of "extended MFG", we hence provide generic results to address these "MFG of controls", before solving the one generated by the cost function of optimal trading. We provide a closed form formula of its solution, and address the case of "heterogenous preferences" (when each participant has a different risk aversion). Last but not least we give conditions under which participants do not need to instantaneously know the state of the whole system, but can "learn" it day after day, observing others' behaviors.

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

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2021: 6; 2022: 2; 2023: 2; 2024: 5; 2025: 3; 2026: 5.

23 papers.

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  1. 2021Generalization in Mean Field Games by Learning Master Policiescited by 28
  2. 2021Deep Learning for Mean Field Games and Mean Field Control with Applications to Financecited by 20
  3. 2022Bridging Mean-Field Games and Normalizing Flows with Trajectory Regularizationcited by 17
  4. 2021Reinforcement Learning for Mean Field Games, with Applications to Economicscited by 15
  5. 2023On the Statistical Efficiency of Mean-Field Reinforcement Learning with General Function Approximationcited by 14
  6. 2021Signatured Deep Fictitious Play for Mean Field Games with Common Noisecited by 12
  7. 2022Individual-Level Inverse Reinforcement Learning for Mean Field Gamescited by 10
  8. 2024Model-Based RL for Mean-Field Games is not Statistically Harder than Single-Agent RLcited by 9
  9. 2021Deep Neural Network Algorithms for Parabolic PIDEs and Applications in Insurance Mathematicscited by 5
  10. 2021Deep Learning for Principal-Agent Mean Field Gamescited by 5
  11. 2024Independent RL for Cooperative-Competitive Agents: A Mean-Field Perspectivecited by 3
  12. 2025Learning Surrogate Potential Mean Field Games via Gaussian Processes: A Data-Driven Approach to Ill-Posed Inverse Problemscited by 2
11 more
  1. 2025Solving Continuous Mean Field Games: Deep Reinforcement Learning for Non-Stationary Dynamicscited by 2
  2. 2023Deep Learning for Mean Field Games with non-separable Hamiltonianscited by 1
  3. 2026Bench-MFG: A Benchmark Suite for Learning in Stationary Mean Field Gamescited by 1
  4. 2024Learning Macroeconomic Policies through Dynamic Stackelberg Mean-Field Gamescited by 0
  5. 2024Mean-field Chaos Diffusion Modelscited by 0
  6. 2024Graphon Particle Systems, Part II: Dynamics of Distributed Stochastic Continuum Optimizationcited by 0
  7. 2025Consensus Based Stochastic Controlcited by 0
  8. 2026Recurrent Structural Policy Gradient for Partially Observable Mean Field Gamescited by 0
  9. 2026Recursive Maximum Likelihood Estimation for Interacting Particle Systems using Virtual Particlescited by 0
  10. 2026Towards Model-Free Learning in Dynamic Population Games: An Application to Karma Economiescited by 0
  11. 2026Neural Parameter Calibration for Finite-State Mean Field Gamescited by 0