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Regularity for weak solutions to first-order local mean field games
AbdulRahman M. Alharbi, Giuseppe Di Fazio, Diogo A. Gomes and Melih Ucer Nonlinear Differential Equations and Applications NoDEA 32(5) (2025) https://doi.org/10.1007/s00030-025-01099-7
Weak-strong uniqueness for solutions to mean-field games
Rita Ferreira, Diogo Gomes and Vardan Voskanyan Proceedings of the American Mathematical Society 153(8) 3363 (2025) https://doi.org/10.1090/proc/17208
The Convergence Rate of Vanishing Viscosity Approximations for 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
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
Weak solutions for potential mean field games of controls
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
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
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 84 541 (2018) https://doi.org/10.1007/978-3-319-56436-4_7
Optimal density evolution with congestion: L∞ bounds via flow interchange techniques and applications to variational Mean Field Games
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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
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
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
Existence and Uniqueness of Solutions for Bertrand and Cournot Mean Field Games
Probabilistic Theory of Mean Field Games with Applications II
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One-Dimensional Stationary Mean-Field Games with Local Coupling
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
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
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
Two Numerical Approaches to Stationary Mean-Field Games
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
Metric gradient flows with state dependent functionals: The Nash-MFG equilibrium flows and their numerical schemes
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
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
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
A variational approach to second order mean field games with density constraints: The stationary case
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