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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
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
Convergence of some Mean Field Games systems to aggregation and flocking models
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
New estimates on the regularity of the pressure in density‐constrained mean field games
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
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
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
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
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
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