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

scholarly journals An entropy minimization approach to second-order variational mean-field games

2019 ◽  
Vol 29 (08) ◽  
pp. 1553-1583 ◽  
Author(s):  
Jean-David Benamou ◽  
Guillaume Carlier ◽  
Simone Di Marino ◽  
Luca Nenna
Keyword(s):  
Efficient Algorithm ◽  
Mean Field ◽  
Time Discretization ◽  
Second Order ◽  
Mean Field Games ◽  
Time Step ◽  
Entropy Minimization ◽  
Convergence Results ◽  
Quadratic Hamiltonian ◽  
Minimization Approach

We propose an entropy minimization viewpoint on variational mean-field games with diffusion and quadratic Hamiltonian. We carefully analyze the time discretization of such problems, establish [Formula: see text]-convergence results as the time step vanishes and propose an efficient algorithm relying on this entropic interpretation as well as on the Sinkhorn scaling algorithm.

scholarly journals Controlled diffusion Mean Field Games with common noise and McKean-Vlasov second order backward SDEs

2021 ◽  
Vol 66 (4) ◽  
pp. 774-805
Author(s):  
Adrien Barrasso ◽  
Adrien Barrasso ◽  
Nizar Touzi ◽  
Nizar Touzi
Keyword(s):  
Mean Field ◽  
Second Order ◽  
Mean Field Games ◽  
Controlled Diffusion ◽  
Common Noise ◽  
Backward Sdes

Рассматривается игра среднего поля с одним внешним шумом, коэффициент диффузии которого включает управление. Доказывается существование слабого решения с релаксацией при некоторых условиях на коэффициент диффузии. Далее, показывается, что при отсутствии этого внешнего шума игра среднего поля описывается обратным стохастическим дифференциальным уравнением типа Маккина-Власова второго порядка.

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 Regularity for second order stationary mean-field games

2017 ◽  
Vol 66 (1) ◽  
pp. 1-22 ◽  
Author(s):  
Edgard Pimentel ◽  
Vardan Voskanyan
Keyword(s):  
Mean Field ◽  
Second Order ◽  
Mean Field Games
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