scholarly journals On the Variational Formulation of Some Stationary Second-Order Mean Field Games Systems

2018 ◽  
Vol 50 (1) ◽  
pp. 1255-1277 ◽  
Author(s):  
Alpár Richárd Mészáros ◽  
Francisco J. Silva
Keyword(s):  
Variational Formulation ◽  
Mean Field ◽  
Second Order ◽  
Mean Field Games

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 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

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 Lax connection and conserved quantities of quadratic mean field games

2021 ◽  
Vol 62 (8) ◽  
pp. 083302
Author(s):  
Thibault Bonnemain ◽  
Thierry Gobron ◽  
Denis Ullmo
Keyword(s):  
Mean Field ◽  
Mean Field Games ◽  
Conserved Quantities ◽  
Quadratic Mean

scholarly journals Quantum Mean-Field Games with the Observations of Counting Type

Games ◽  
2021 ◽  
Vol 12 (1) ◽  
pp. 7
Author(s):  
Vassili N. Kolokoltsov
Keyword(s):  
Game Theory ◽  
Nash Equilibrium ◽  
Open Problem ◽  
Existence And Uniqueness ◽  
Existence Of Solutions ◽  
Mean Field ◽  
Mean Field Games ◽  
Quantum Game ◽  
Quantum Games ◽  
Interesting Open Problem

Quantum games and mean-field games (MFG) represent two important new branches of game theory. In a recent paper the author developed quantum MFGs merging these two branches. These quantum MFGs were based on the theory of continuous quantum observations and filtering of diffusive type. In the present paper we develop the analogous quantum MFG theory based on continuous quantum observations and filtering of counting type. However, proving existence and uniqueness of the solutions for resulting limiting forward-backward system based on jump-type processes on manifolds seems to be more complicated than for diffusions. In this paper we only prove that if a solution exists, then it gives an ϵ-Nash equilibrium for the corresponding N-player quantum game. The existence of solutions is suggested as an interesting open problem.

Linear–Quadratic Time-Inconsistent Mean Field Games

2013 ◽  
Vol 3 (4) ◽  
pp. 537-552 ◽  
Author(s):  
A. Bensoussan ◽  
K. C. J. Sung ◽  
S. C. P. Yam
Keyword(s):  
Mean Field ◽  
Mean Field Games ◽  
Linear Quadratic ◽  
Time Inconsistent
Sign in / Sign up

Export Citation Format

Share Document