Learning in mean field games: The fictitious play
ESAIM: COCV, 23 2 (2017) 569-591
Published online: 2017-01-18
Articles citing this article
The Citing articles tool gives a list of articles citing the current article.
The citing articles come from EDP Sciences database, as well as other publishers participating in CrossRef Cited-by Linking Program. You can set up your personal account to receive an email alert each time this article is cited by a new article (see the menu on the right-hand side of the abstract page).
Cited article:
This article has been cited by the following article(s):
Learning Equilibria in Cournot Mean Field Games of Controls
Fabio Camilli, Mathieu Laurière and Qing TangSIAM Journal on Control and Optimization 63 (2) 1407 (2025)
https://doi.org/10.1137/24M1662643
Strong solutions to submodular mean field games with common noise and related McKean–Vlasov FBSDEs
Jodi DianettiThe Annals of Applied Probability 35 (3) (2025)
https://doi.org/10.1214/25-AAP2151
Multiple equilibria in mean-field game models of firm competition with strategic complementarities
Jodi Dianetti, Salvatore Federico, Giorgio Ferrari and Giuseppe FloccariQuantitative Finance 25 (3) 343 (2025)
https://doi.org/10.1080/14697688.2024.2438217
Approximation and perturbations of stable solutions to a stationary mean field game system
Jules Berry, Olivier Ley and Francisco J. SilvaJournal de Mathématiques Pures et Appliquées 194 103666 (2025)
https://doi.org/10.1016/j.matpur.2025.103666
Exploration Noise for Learning Linear-Quadratic Mean Field Games
François Delarue and Athanasios VasileiadisMathematics of Operations Research (2024)
https://doi.org/10.1287/moor.2021.0157
Mean field games of controls with Dirichlet boundary conditions
Mattia Bongini and Francesco SalvaraniESAIM: Control, Optimisation and Calculus of Variations 30 32 (2024)
https://doi.org/10.1051/cocv/2024020
Dynamics of market making algorithms in dealer markets: Learning and tacit collusion
Rama Cont and Wei XiongMathematical Finance 34 (2) 467 (2024)
https://doi.org/10.1111/mafi.12401
Approximation of Deterministic Mean Field Games with Control-Affine Dynamics
Justina Gianatti and Francisco J. SilvaFoundations of Computational Mathematics 24 (6) 2017 (2024)
https://doi.org/10.1007/s10208-023-09629-4
Coupled Alternating Neural Networks for Solving Multi-Population High-Dimensional Mean-Field Games
Guofang Wang, Jing Fang, Lulu Jiang, Wang Yao and Ning LiMathematics 12 (23) 3803 (2024)
https://doi.org/10.3390/math12233803
50 (2024)
https://doi.org/10.1287/educ.2024.0272
Deep Policy Iteration for high-dimensional mean field games
Mouhcine Assouli and Badr MissaouiApplied Mathematics and Computation 481 128923 (2024)
https://doi.org/10.1016/j.amc.2024.128923
Actor-Critic Reinforcement Learning Algorithms for Mean Field Games in Continuous Time, State and Action Spaces
Hong Liang, Zhiping Chen and Kaili JingApplied Mathematics & Optimization 89 (3) (2024)
https://doi.org/10.1007/s00245-024-10138-1
A Mean Field Game Model for Renewable Investment Under Long-Term Uncertainty and Risk Aversion
Célia Escribe, Josselin Garnier and Emmanuel GobetDynamic Games and Applications 14 (5) 1093 (2024)
https://doi.org/10.1007/s13235-024-00554-x
Learning Optimal Policies in Potential Mean Field Games: Smoothed Policy Iteration Algorithms
Qing Tang and Jiahao SongSIAM Journal on Control and Optimization 62 (1) 351 (2024)
https://doi.org/10.1137/22M1539861
Recent developments in machine learning methods for stochastic control and games
Ruimeng Hu and Mathieu LaurièreNumerical Algebra, Control and Optimization (2024)
https://doi.org/10.3934/naco.2024031
A myopic adjustment process for mean field games with finite state and action space
Berenice Anne NeumannInternational Journal of Game Theory 53 (1) 159 (2024)
https://doi.org/10.1007/s00182-023-00866-z
Dealer markets: A reinforcement learning mean field game approach
Martino Bernasconi, E. Vittori, F. Trovò and M. RestelliThe North American Journal of Economics and Finance 68 101974 (2023)
https://doi.org/10.1016/j.najef.2023.101974
High order computation of optimal transport, mean field planning, and potential mean field games
Guosheng Fu, Siting Liu, Stanley Osher and Wuchen LiJournal of Computational Physics 491 112346 (2023)
https://doi.org/10.1016/j.jcp.2023.112346
Discrete potential mean field games: duality and numerical resolution
J. Frédéric Bonnans, Pierre Lavigne and Laurent PfeifferMathematical Programming 202 (1-2) 241 (2023)
https://doi.org/10.1007/s10107-023-01934-8
A Unifying Framework for Submodular Mean Field Games
Jodi Dianetti, Giorgio Ferrari, Markus Fischer and Max NendelMathematics of Operations Research 48 (3) 1679 (2023)
https://doi.org/10.1287/moor.2022.1316
Policy Iteration Method for Time-Dependent Mean Field Games Systems with Non-separable Hamiltonians
Mathieu Laurière, Jiahao Song and Qing TangApplied Mathematics & Optimization 87 (2) (2023)
https://doi.org/10.1007/s00245-022-09925-5
Approximation of deterministic mean field games under polynomial growth conditions on the data
Justina Gianatti, Francisco J. Silva and Ahmad ZorkotJournal of Dynamics and Games (2023)
https://doi.org/10.3934/jdg.2023018
Mean-field game analysis of crowd evacuation using the Cristiani-Santo-Menci method
Ryosuke Yano and Hisayasu KurodaPhysical Review E 108 (1) (2023)
https://doi.org/10.1103/PhysRevE.108.014119
Partially Centralized Model-Predictive Mean Field Games for controlling multi-agent systems
Daisuke Inoue, Yuji Ito, Takahito Kashiwabara, Norikazu Saito and Hiroaki YoshidaIFAC Journal of Systems and Control 24 100217 (2023)
https://doi.org/10.1016/j.ifacsc.2023.100217
13936 361 (2023)
https://doi.org/10.1007/978-3-031-33377-4_28
A fictitious-play finite-difference method for linearly solvable mean field games
Daisuke Inoue, Yuji Ito, Takahito Kashiwabara, Norikazu Saito and Hiroaki YoshidaESAIM: Mathematical Modelling and Numerical Analysis 57 (4) 1863 (2023)
https://doi.org/10.1051/m2an/2023026
Rates of convergence for the policy iteration method for Mean Field Games systems
Fabio Camilli and Qing TangJournal of Mathematical Analysis and Applications 512 (1) 126138 (2022)
https://doi.org/10.1016/j.jmaa.2022.126138
Unified reinforcement Q-learning for mean field game and control problems
Andrea Angiuli, Jean-Pierre Fouque and Mathieu LaurièreMathematics of Control, Signals, and Systems 34 (2) 217 (2022)
https://doi.org/10.1007/s00498-021-00310-1
Entropy Regularization for Mean Field Games with Learning
Xin Guo, Renyuan Xu and Thaleia ZariphopoulouMathematics of Operations Research 47 (4) 3239 (2022)
https://doi.org/10.1287/moor.2021.1238
A Novel Mean-Field-Game-Type Optimal Control for Very Large-Scale Multiagent Systems
Zejian Zhou and Hao XuIEEE Transactions on Cybernetics 52 (6) 5197 (2022)
https://doi.org/10.1109/TCYB.2020.3028267
Monotone Solutions of the Master Equation for Mean Field Games with Idiosyncratic Noise
Pierre Cardaliaguet and Panagiotis SouganidisSIAM Journal on Mathematical Analysis 54 (4) 4198 (2022)
https://doi.org/10.1137/21M1450008
Recent Developments in Machine Learning Methods for Stochastic Control and Games
Ruimeng Hu and Mathieu LauriereSSRN Electronic Journal (2022)
https://doi.org/10.2139/ssrn.4096569
Dynamics of Market Making Algorithms in Dealer Markets: Learning and Tacit Collusion
Rama Cont and Wei XIONGSSRN Electronic Journal (2022)
https://doi.org/10.2139/ssrn.4119858
Random features for high-dimensional nonlocal mean-field games
Sudhanshu Agrawal, Wonjun Lee, Samy Wu Fung and Levon NurbekyanJournal of Computational Physics 459 111136 (2022)
https://doi.org/10.1016/j.jcp.2022.111136
Convergence of deep fictitious play for stochastic differential games
Jiequn Han, Ruimeng Hu and Jihao LongFrontiers of Mathematical Finance 1 (2) 287 (2022)
https://doi.org/10.3934/fmf.2021011
On first order mean field game systems with a common noise
Pierre Cardaliaguet and Panagiotis E. SouganidisThe Annals of Applied Probability 32 (3) (2022)
https://doi.org/10.1214/21-AAP1734
Mean-field games of finite-fuel capacity expansion with singular controls
Luciano Campi, Tiziano De Angelis, Maddalena Ghio and Giulia LivieriThe Annals of Applied Probability 32 (5) (2022)
https://doi.org/10.1214/21-AAP1771
Hypergraphon mean field games
Kai Cui, Wasiur R. KhudaBukhsh and Heinz KoepplChaos: An Interdisciplinary Journal of Nonlinear Science 32 (11) (2022)
https://doi.org/10.1063/5.0093758
Semiconcavity and sensitivity analysis in mean-field optimal control and applications
Benoît Bonnet and Hélène FrankowskaJournal de Mathématiques Pures et Appliquées 157 282 (2022)
https://doi.org/10.1016/j.matpur.2021.11.001
On the Asymptotic Nature of First Order Mean Field Games
Markus Fischer and Francisco J. SilvaApplied Mathematics & Optimization 84 (2) 2327 (2021)
https://doi.org/10.1007/s00245-020-09711-1
Schauder Estimates for a Class of Potential Mean Field Games of Controls
J. Frédéric Bonnans, Saeed Hadikhanloo and Laurent PfeifferApplied Mathematics & Optimization 83 (3) 1431 (2021)
https://doi.org/10.1007/s00245-019-09592-z
Linearly Solvable Mean-Field Traffic Routing Games
Takashi Tanaka, Ehsan Nekouei, Ali Reza Pedram and Karl Henrik JohanssonIEEE Transactions on Automatic Control 66 (2) 880 (2021)
https://doi.org/10.1109/TAC.2020.2986195
Splitting methods for a class of non-potential mean field games
Siting Liu and Levon NurbekyanJournal of Dynamics & Games 8 (4) 467 (2021)
https://doi.org/10.3934/jdg.2021014
Spatially Inhomogeneous Evolutionary Games
Luigi Ambrosio, Massimo Fornasier, Marco Morandotti and Giuseppe SavaréCommunications on Pure and Applied Mathematics 74 (7) 1353 (2021)
https://doi.org/10.1002/cpa.21995
Submodular mean field games: Existence and approximation of solutions
Jodi Dianetti, Giorgio Ferrari, Markus Fischer and Max NendelThe Annals of Applied Probability 31 (6) (2021)
https://doi.org/10.1214/20-AAP1655
Convergence of some Mean Field Games systems to aggregation and flocking models
Martino Bardi and Pierre CardaliaguetNonlinear Analysis 204 112199 (2021)
https://doi.org/10.1016/j.na.2020.112199
Mean-field Analysis of Multipopulation Dynamics with Label Switching
Marco Morandotti and Francesco SolombrinoSIAM Journal on Mathematical Analysis 52 (2) 1427 (2020)
https://doi.org/10.1137/19M1273426
Non-coercive first order Mean Field Games
Paola Mannucci, Claudio Marchi, Carlo Mariconda and Nicoletta TchouJournal of Differential Equations 269 (5) 4503 (2020)
https://doi.org/10.1016/j.jde.2020.03.035
2278 (2020)
https://doi.org/10.1109/CDC42340.2020.9304279
Fokker-Planck equations of jumping particles and mean field games of impulse control
Charles BertucciAnnales de l'Institut Henri Poincaré C, Analyse non linéaire 37 (5) 1211 (2020)
https://doi.org/10.1016/j.anihpc.2020.04.006
Deterministic mean field games with control on the acceleration
Yves Achdou, Paola Mannucci, Claudio Marchi and Nicoletta TchouNonlinear Differential Equations and Applications NoDEA 27 (3) (2020)
https://doi.org/10.1007/s00030-020-00634-y
Numerical method for FBSDEs of McKean–Vlasov type
Jean-François Chassagneux, Dan Crisan and François DelarueThe Annals of Applied Probability 29 (3) (2019)
https://doi.org/10.1214/18-AAP1429
Finite Mean Field Games: Fictitious play and convergence to a first order continuous mean field game
Saeed Hadikhanloo and Francisco J. SilvaJournal de Mathématiques Pures et Appliquées 132 369 (2019)
https://doi.org/10.1016/j.matpur.2019.02.006
1231 (2019)
https://doi.org/10.1109/CDC40024.2019.9029699
Probabilistic Theory of Mean Field Games with Applications II
René Carmona and François DelarueProbability Theory and Stochastic Modelling, Probabilistic Theory of Mean Field Games with Applications II 84 155 (2018)
https://doi.org/10.1007/978-3-319-56436-4_3
Probabilistic Theory of Mean Field Games with Applications II
René Carmona and François DelarueProbability Theory and Stochastic Modelling, Probabilistic Theory of Mean Field Games with Applications II 84 3 (2018)
https://doi.org/10.1007/978-3-319-56436-4_1
Probabilistic Theory of Mean Field Games with Applications II
René Carmona and François DelarueProbability Theory and Stochastic Modelling, Probabilistic Theory of Mean Field Games with Applications II 84 107 (2018)
https://doi.org/10.1007/978-3-319-56436-4_2
Probabilistic Theory of Mean Field Games with Applications II
René Carmona and François DelarueProbability Theory and Stochastic Modelling, Probabilistic Theory of Mean Field Games with Applications II 84 447 (2018)
https://doi.org/10.1007/978-3-319-56436-4_6
A mean-field game model for homogeneous flocking
Piyush Grover, Kaivalya Bakshi and Evangelos A. TheodorouChaos: An Interdisciplinary Journal of Nonlinear Science 28 (6) (2018)
https://doi.org/10.1063/1.5036663
PDE Models for Multi-Agent Phenomena
Elisabetta Carlini and Francisco J. SilvaSpringer INdAM Series, PDE Models for Multi-Agent Phenomena 28 195 (2018)
https://doi.org/10.1007/978-3-030-01947-1_9
Mean field game of controls and an application to trade crowding
Pierre Cardaliaguet and Charles-Albert LehalleMathematics and Financial Economics 12 (3) 335 (2018)
https://doi.org/10.1007/s11579-017-0206-z
Probabilistic Theory of Mean Field Games with Applications II
René Carmona and François DelarueProbability Theory and Stochastic Modelling, Probabilistic Theory of Mean Field Games with Applications II 84 323 (2018)
https://doi.org/10.1007/978-3-319-56436-4_5
Probabilistic Theory of Mean Field Games with Applications II
René Carmona and François DelarueProbability Theory and Stochastic Modelling, Probabilistic Theory of Mean Field Games with Applications II 84 541 (2018)
https://doi.org/10.1007/978-3-319-56436-4_7
Probabilistic Theory of Mean Field Games with Applications II
René Carmona and François DelarueProbability Theory and Stochastic Modelling, Probabilistic Theory of Mean Field Games with Applications II 84 239 (2018)
https://doi.org/10.1007/978-3-319-56436-4_4
Stable solutions in potential mean field game systems
Ariela Briani and Pierre CardaliaguetNonlinear Differential Equations and Applications NoDEA 25 (1) (2018)
https://doi.org/10.1007/s00030-017-0493-3
On the Discretization of Some Nonlinear Fokker--Planck--Kolmogorov Equations and Applications
Elisabetta Carlini and Francisco J. SilvaSIAM Journal on Numerical Analysis 56 (4) 2148 (2018)
https://doi.org/10.1137/17M1143022
Preconditioning the Augmented Lagrangian Method for Instationary Mean Field Games with Diffusion
Roman AndreevSIAM Journal on Scientific Computing 39 (6) A2763 (2017)
https://doi.org/10.1137/16M1072346
Mean Field Control Hierarchy
Giacomo Albi, Young-Pil Choi, Massimo Fornasier and Dante KaliseApplied Mathematics & Optimization 76 (1) 93 (2017)
https://doi.org/10.1007/s00245-017-9429-x