scholarly journals Asymptotic analysis of mean field games with small common noise

2018 ◽  
Vol 106 (3-4) ◽  
pp. 205-232
Author(s):  
Saran Ahuja ◽  
Weiluo Ren ◽  
Tzu-Wei Yang
Keyword(s):  
Asymptotic Analysis ◽  
Mean Field ◽  
Mean Field Games ◽  
Common Noise

scholarly journals On mean field games with common noise and McKean-Vlasov SPDEs

2019 ◽  
Vol 37 (4) ◽  
pp. 522-549 ◽  
Author(s):  
Vassili N. Kolokoltsov ◽  
Marianna Troeva
Keyword(s):  
Mean Field ◽  
Mean Field Games ◽  
Common Noise

Mean Field Game System with a Common Noise

2019 ◽  
pp. 85-127
Author(s):  
Pierre Cardaliaguet ◽  
François Delarue ◽  
Jean-Michel Lasry ◽  
Pierre-Louis Lions
Keyword(s):  
Existence And Uniqueness ◽  
Mean Field ◽  
Mean Field Games ◽  
Random Functions ◽  
Common Noise ◽  
The Common ◽  
The Mean ◽  
Random Flow ◽  
Uniqueness Of A Solution ◽  
Classical Strategy

This chapter talks about the unique solvability of the mean field games (MFGs) system with common noise. In terms of a game with a finite number of players, the common noise describes some noise that affects all the players in the same way, so that the dynamics of one given particle reads a certain master equation. It explains the use of the standard convention from the theory of stochastic processes that consists in indicating the time parameter as an index in random functions. Using a continuation like argument instead of the classical strategy based on the Schauder fixed-point theorem, this chapter investigates the existence and uniqueness of a solution. It discusses the effect of the common noise in randomizing the MFG equilibria so that it becomes a random flow of measures.

scholarly journals Mean field games with common noise

2016 ◽  
Vol 44 (6) ◽  
pp. 3740-3803 ◽  
Author(s):  
René Carmona ◽  
François Delarue ◽  
Daniel Lacker
Keyword(s):  
Mean Field ◽  
Mean Field Games ◽  
Common Noise

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 Continuous-Time Mean Field Games with Finite State Space and Common Noise

2021 ◽  
Author(s):  
Christoph Belak ◽  
Daniel Hoffmann ◽  
Frank T. Seifried
Keyword(s):  
Continuous Time ◽  
Mean Field ◽  
Mean Field Games ◽  
Mathematical Framework ◽  
Equilibrium System ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
State Process ◽  
Common Noise ◽  
Appl Math

AbstractWe formulate and analyze a mathematical framework for continuous-time mean field games with finitely many states and common noise, including a rigorous probabilistic construction of the state process and existence and uniqueness results for the resulting equilibrium system. The key insight is that we can circumvent the master equation and reduce the mean field equilibrium to a system of forward-backward systems of (random) ordinary differential equations by conditioning on common noise events. In the absence of common noise, our setup reduces to that of Gomes, Mohr and Souza (Appl Math Optim 68(1): 99–143, 2013) and Cecchin and Fischer (Appl Math Optim 81(2):253–300, 2020).

Sign in / Sign up

Export Citation Format

Share Document