scholarly journals Fokker-Planck equations of jumping particles and mean field games of impulse control

2020 ◽  
Vol 37 (5) ◽  
pp. 1211-1244
Author(s):  
Charles Bertucci
Keyword(s):  
Impulse Control ◽  
Mean Field ◽  
Mean Field Games ◽  
Fokker Planck Equations ◽  
Fokker Planck

scholarly journals General properties of nonlinear mean field Fokker-Planck equations

2007 ◽  
Author(s):  
P. H. Chavanis ◽  
Sumiyoshi Abe ◽  
Hans Herrmann ◽  
Piero Quarati ◽  
Andrea Rapisarda ◽  
...  
Keyword(s):  
Mean Field ◽  
General Properties ◽  
Fokker Planck Equations ◽  
Fokker Planck

scholarly journals A Quadratic Mean Field Games Model for the Langevin Equation

Axioms ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 68
Author(s):  
Fabio Camilli
Keyword(s):  
Langevin Equation ◽  
Existence Result ◽  
Mean Field ◽  
Mean Field Games ◽  
Existence Of A Solution ◽  
Quadratic Mean ◽  
Change Of Variables ◽  
The Mean ◽  
The Cost ◽  
Fokker Planck Equations

We consider a Mean Field Games model where the dynamics of the agents is given by a controlled Langevin equation and the cost is quadratic. An appropriate change of variables transforms the Mean Field Games system into a system of two coupled kinetic Fokker–Planck equations. We prove an existence result for the latter system, obtaining consequently existence of a solution for the Mean Field Games system.

scholarly journals A remark on Uzawa’s algorithm and an application to mean field games systems

2020 ◽  
Vol 54 (3) ◽  
pp. 1053-1071
Author(s):  
Charles Bertucci
Keyword(s):  
Optimal Stopping ◽  
Impulse Control ◽  
Mean Field ◽  
Numerical Results ◽  
Mean Field Games ◽  
General Situation ◽  
Continuous Control ◽  
The One

In this paper, we present an extension of Uzawa’s algorithm and apply it to build approximating sequences of mean field games systems. We prove that Uzawa’s iterations can be used in a more general situation than the one in it is usually used. We then present some numerical results of those iterations on discrete mean field games systems of optimal stopping, impulse control and continuous control.

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