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:

Entropy-minimizing dynamical transport on Riemannian manifolds

Gabriele Bocchi and Alessio Porretta
Calculus of Variations and Partial Differential Equations 64 (2) (2025)
https://doi.org/10.1007/s00526-024-02920-4

Mean Field Games Systems under Displacement Monotonicity

Alpár R. Mészáros and Chenchen Mou
SIAM Journal on Mathematical Analysis 56 (1) 529 (2024)
https://doi.org/10.1137/22M1534353

Coupled Alternating Neural Networks for Solving Multi-Population High-Dimensional Mean-Field Games

Guofang Wang, Jing Fang, Lulu Jiang, Wang Yao and Ning Li
Mathematics 12 (23) 3803 (2024)
https://doi.org/10.3390/math12233803

Regularity and Long Time Behavior of One-Dimensional First-Order Mean Field Games and the Planning Problem

Nikiforos Mimikos-Stamatopoulos and Sebastian Munoz
SIAM Journal on Mathematical Analysis 56 (1) 43 (2024)
https://doi.org/10.1137/23M1547779

An optimal control problem for the continuity equation arising in smart charging

Adrien Séguret
Journal of Mathematical Analysis and Applications 531 (1) 127891 (2024)
https://doi.org/10.1016/j.jmaa.2023.127891

On Numerical Approximations of Fractional and Nonlocal Mean Field Games

Indranil Chowdhury, Olav Ersland and Espen R. Jakobsen
Foundations of Computational Mathematics 23 (4) 1381 (2023)
https://doi.org/10.1007/s10208-022-09572-w

A fast proximal gradient method and convergence analysis for dynamic mean field planning

Jiajia Yu, Rongjie Lai, Wuchen Li and Stanley Osher
Mathematics of Computation 93 (346) 603 (2023)
https://doi.org/10.1090/mcom/3879

Hybrid control for optimal visiting problems for a single player and for a crowd

Fabio Bagagiolo, Adriano Festa and Luciano Marzufero
Nonlinear Differential Equations and Applications NoDEA 29 (1) (2022)
https://doi.org/10.1007/s00030-021-00737-0

A variational approach to first order kinetic mean field games with local couplings

Megan Griffin-Pickering and Alpár R. Mészáros
Communications in Partial Differential Equations 47 (10) 1945 (2022)
https://doi.org/10.1080/03605302.2022.2101003

Selection by vanishing common noise for potential finite state mean field games

Alekos Cecchin and François Delarue
Communications in Partial Differential Equations 47 (1) 89 (2022)
https://doi.org/10.1080/03605302.2021.1955256

Comparing the best-reply strategy and mean-field games: The stationary case

MATT BARKER, PIERRE DEGOND and MARIE-THERESE WOLFRAM
European Journal of Applied Mathematics 33 (1) 79 (2022)
https://doi.org/10.1017/S0956792520000376

A Multi-Population Mean-Field Game Approach for Large-Scale Agents Cooperative Attack-Defense Evolution in High-Dimensional Environments

Guofang Wang, Ziming Li, Wang Yao and Sikai Xia
Mathematics 10 (21) 4075 (2022)
https://doi.org/10.3390/math10214075

Nonlocal Bertrand and Cournot mean field games with general nonlinear demand schedule

P. Jameson Graber, Vincenzo Ignazio and Ariel Neufeld
Journal de Mathématiques Pures et Appliquées 148 150 (2021)
https://doi.org/10.1016/j.matpur.2021.02.002

A mean field game model for the evolution of cities

César Barilla, Guillaume Carlier and Jean-Michel Lasry
Journal of Dynamics & Games 8 (3) 299 (2021)
https://doi.org/10.3934/jdg.2021017

Alternating the population and control neural networks to solve high-dimensional stochastic mean-field games

Alex Tong Lin, Samy Wu Fung, Wuchen Li, Levon Nurbekyan and Stanley J. Osher
Proceedings of the National Academy of Sciences 118 (31) (2021)
https://doi.org/10.1073/pnas.2024713118

On some singular mean-field games

Marco Cirant, Diogo A. Gomes, Edgard A. Pimentel and Héctor Sánchez-Morgado
Journal of Dynamics & Games 8 (4) 445 (2021)
https://doi.org/10.3934/jdg.2021006

Weak solutions for potential mean field games of controls

P. Jameson Graber, Alan Mullenix and Laurent Pfeiffer
Nonlinear Differential Equations and Applications NoDEA 28 (5) (2021)
https://doi.org/10.1007/s00030-021-00712-9

Closed-Loop Equilibrium for Time-Inconsistent McKean--Vlasov Controlled Problem

Hongwei Mei and Chao Zhu
SIAM Journal on Control and Optimization 58 (6) 3842 (2020)
https://doi.org/10.1137/20M1319796

A variational approach to the mean field planning problem

Carlo Orrieri, Alessio Porretta and Giuseppe Savaré
Journal of Functional Analysis 277 (6) 1868 (2019)
https://doi.org/10.1016/j.jfa.2019.04.011

Contemporary Research in Elliptic PDEs and Related Topics

Annalisa Cesaroni and Marco Cirant
Springer INdAM Series, Contemporary Research in Elliptic PDEs and Related Topics 33 221 (2019)
https://doi.org/10.1007/978-3-030-18921-1_5

On the Existence and Uniqueness of Solutions to Time-Dependent Fractional MFG

Marco Cirant and Alessandro Goffi
SIAM Journal on Mathematical Analysis 51 (2) 913 (2019)
https://doi.org/10.1137/18M1216420

The planning problem in mean field games as regularized mass transport

P. Jameson Graber, Alpár R. Mészáros, Francisco J. Silva and Daniela Tonon
Calculus of Variations and Partial Differential Equations 58 (3) (2019)
https://doi.org/10.1007/s00526-019-1561-9

New estimates on the regularity of the pressure in density‐constrained mean field games

Hugo Lavenant and Filippo Santambrogio
Journal of the London Mathematical Society 100 (2) 644 (2019)
https://doi.org/10.1112/jlms.12245

Restoring uniqueness to mean-field games by randomizing the equilibria

François Delarue
Stochastics and Partial Differential Equations: Analysis and Computations 7 (4) 598 (2019)
https://doi.org/10.1007/s40072-019-00135-9

Optimal density evolution with congestion: L∞ bounds via flow interchange techniques and applications to variational Mean Field Games

Hugo Lavenant and Filippo Santambrogio
Communications in Partial Differential Equations 43 (12) 1761 (2018)
https://doi.org/10.1080/03605302.2018.1499116

Probabilistic Theory of Mean Field Games with Applications II

René Carmona and François Delarue
Probability 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 I

René Carmona and François Delarue
Probability Theory and Stochastic Modelling, Probabilistic Theory of Mean Field Games with Applications I 83 129 (2018)
https://doi.org/10.1007/978-3-319-58920-6_3

The Initial Value Problem for the Euler Equations of Incompressible Fluids Viewed as a Concave Maximization Problem

Yann Brenier
Communications in Mathematical Physics 364 (2) 579 (2018)
https://doi.org/10.1007/s00220-018-3240-7

Probabilistic Theory of Mean Field Games with Applications II

René Carmona and François Delarue
Probability 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

Existence of Weak Solutions to Stationary Mean-Field Games through Variational Inequalities

Rita Ferreira and Diogo Gomes
SIAM Journal on Mathematical Analysis 50 (6) 5969 (2018)
https://doi.org/10.1137/16M1106705

Probabilistic Theory of Mean Field Games with Applications II

René Carmona and François Delarue
Probability 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

Proximal Methods for Stationary Mean Field Games with Local Couplings

L. M. Bricen͂o-Arias, D. Kalise and F. J. Silva
SIAM Journal on Control and Optimization 56 (2) 801 (2018)
https://doi.org/10.1137/16M1095615

Probabilistic Theory of Mean Field Games with Applications II

René Carmona and François Delarue
Probability 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

One-Dimensional Stationary Mean-Field Games with Local Coupling

Diogo A. Gomes, Levon Nurbekyan and Mariana Prazeres
Dynamic Games and Applications 8 (2) 315 (2018)
https://doi.org/10.1007/s13235-017-0223-9

Sobolev regularity for first order mean field games

P. Jameson Graber and Alpár R. Mészáros
Annales de l'Institut Henri Poincaré C, Analyse non linéaire 35 (6) 1557 (2018)
https://doi.org/10.1016/j.anihpc.2018.01.002

Probabilistic Theory of Mean Field Games with Applications II

René Carmona and François Delarue
Probability 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

First-order, stationary mean-field games with congestion

David Evangelista, Rita Ferreira, Diogo A. Gomes, Levon Nurbekyan and Vardan Voskanyan
Nonlinear Analysis 173 37 (2018)
https://doi.org/10.1016/j.na.2018.03.011

Probabilistic Theory of Mean Field Games with Applications I

René Carmona and François Delarue
Probability Theory and Stochastic Modelling, Probabilistic Theory of Mean Field Games with Applications I 83 513 (2018)
https://doi.org/10.1007/978-3-319-58920-6_6

Probabilistic Theory of Mean Field Games with Applications II

René Carmona and François Delarue
Probability 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 Delarue
Probability 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

Existence and Uniqueness of Solutions for Bertrand and Cournot Mean Field Games

P. Jameson Graber and Alain Bensoussan
Applied Mathematics & Optimization 77 (1) 47 (2018)
https://doi.org/10.1007/s00245-016-9366-0

On the Variational Formulation of Some Stationary Second-Order Mean Field Games Systems

Alpár Richárd Mészáros and Francisco J. Silva
SIAM Journal on Mathematical Analysis 50 (1) 1255 (2018)
https://doi.org/10.1137/17M1125960

Active Particles, Volume 1

Jean-David Benamou, Guillaume Carlier and Filippo Santambrogio
Modeling and Simulation in Science, Engineering and Technology, Active Particles, Volume 1 141 (2017)
https://doi.org/10.1007/978-3-319-49996-3_4

Advances in Dynamic and Mean Field Games

Pierre Cardaliaguet, Alessio Porretta and Daniela Tonon
Annals of the International Society of Dynamic Games, Advances in Dynamic and Mean Field Games 15 49 (2017)
https://doi.org/10.1007/978-3-319-70619-1_3

Metric gradient flows with state dependent functionals: The Nash-MFG equilibrium flows and their numerical schemes

Gabriel Turinici
Nonlinear Analysis 165 163 (2017)
https://doi.org/10.1016/j.na.2017.10.002

Linear Quadratic Mean Field Type Control and Mean Field Games with Common Noise, with Application to Production of an Exhaustible Resource

P. Jameson Graber
Applied Mathematics & Optimization 74 (3) 459 (2016)
https://doi.org/10.1007/s00245-016-9385-x

First Order Mean Field Games with Density Constraints: Pressure Equals Price

Pierre Cardaliaguet, Alpár R. Mészáros and Filippo Santambrogio
SIAM Journal on Control and Optimization 54 (5) 2672 (2016)
https://doi.org/10.1137/15M1029849

Homogenization of a Mean Field Game System in the Small Noise Limit

Annalisa Cesaroni, Nicolas Dirr and Claudio Marchi
SIAM Journal on Mathematical Analysis 48 (4) 2701 (2016)
https://doi.org/10.1137/16M1063459

Sobolev regularity for the first order Hamilton–Jacobi equation

Pierre Cardaliaguet, Alessio Porretta and Daniela Tonon
Calculus of Variations and Partial Differential Equations 54 (3) 3037 (2015)
https://doi.org/10.1007/s00526-015-0893-3

Second order mean field games with degenerate diffusion and local coupling

Pierre Cardaliaguet, P. Jameson Graber, Alessio Porretta and Daniela Tonon
Nonlinear Differential Equations and Applications NoDEA 22 (5) 1287 (2015)
https://doi.org/10.1007/s00030-015-0323-4

A variational approach to second order mean field games with density constraints: The stationary case

Alpár Richárd Mészáros and Francisco J. Silva
Journal de Mathématiques Pures et Appliquées 104 (6) 1135 (2015)
https://doi.org/10.1016/j.matpur.2015.07.008

Augmented Lagrangian Methods for Transport Optimization, Mean Field Games and Degenerate Elliptic Equations

Jean-David Benamou and Guillaume Carlier
Journal of Optimization Theory and Applications 167 (1) 1 (2015)
https://doi.org/10.1007/s10957-015-0725-9