Introduction to Variational Methods for Viscous Ergodic Mean-Field Games with Local Coupling

2019 ◽  
pp. 221-246 ◽  
Author(s):  
Annalisa Cesaroni ◽  
Marco Cirant
Keyword(s):  
Variational Methods ◽  
Mean Field ◽  
Mean Field Games ◽  
Local Coupling ◽  
Ergodic Mean

scholarly journals Weak KAM Approach to First-Order Mean Field Games with State Constraints

2021 ◽  
Author(s):  
Piermarco Cannarsa ◽  
Wei Cheng ◽  
Cristian Mendico ◽  
Kaizhi Wang
Keyword(s):  
Time Horizon ◽  
State Constraints ◽  
Kam Theory ◽  
Mean Field ◽  
Mean Field Games ◽  
Asymptotic Behavior Of Solutions ◽  
Weak Kam Theory ◽  
First Order ◽  
Jacobi Equations ◽  
Ergodic Mean

AbstractWe study the asymptotic behavior of solutions to the constrained MFG system as the time horizon T goes to infinity. For this purpose, we analyze first Hamilton–Jacobi equations with state constraints from the viewpoint of weak KAM theory, constructing a Mather measure for the associated variational problem. Using these results, we show that a solution to the constrained ergodic mean field games system exists and the ergodic constant is unique. Finally, we prove that any solution of the first-order constrained MFG problem on [0, T] converges to the solution of the ergodic system as T goes to infinity.

scholarly journals One-Dimensional Stationary Mean-Field Games with Local Coupling

2017 ◽  
Vol 8 (2) ◽  
pp. 315-351 ◽  
Author(s):  
Diogo A. Gomes ◽  
Levon Nurbekyan ◽  
Mariana Prazeres
Keyword(s):  
Mean Field ◽  
Mean Field Games ◽  
One Dimensional ◽  
Local Coupling

scholarly journals Second order mean field games with degenerate diffusion and local coupling

2015 ◽  
Vol 22 (5) ◽  
pp. 1287-1317 ◽  
Author(s):  
Pierre Cardaliaguet ◽  
P. Jameson Graber ◽  
Alessio Porretta ◽  
Daniela Tonon
Keyword(s):  
Mean Field ◽  
Second Order ◽  
Mean Field Games ◽  
Degenerate Diffusion ◽  
Local Coupling
Sign in / Sign up

Export Citation Format

Share Document