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Global well-posedness of first-order mean field games and master equations with nonlinear dynamics
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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
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
A mean field game model for the evolution of cities
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
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
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
Concentration of ground states in stationary mean-field games systems
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
Optimal density evolution with congestion: L∞ bounds via flow interchange techniques and applications to variational Mean Field Games
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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
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
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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
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Sobolev regularity for first order mean field games
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One-Dimensional Stationary Mean-Field Games with Local Coupling
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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 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 84 155 (2018) https://doi.org/10.1007/978-3-319-56436-4_3
Two Numerical Approaches to Stationary 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
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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
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
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