Master Equation for Finite State Mean Field Games with Additive Common Noise

2020 ◽  
pp. 203-248
Author(s):  
François Delarue
Keyword(s):  
Master Equation ◽  
Mean Field ◽  
Mean Field Games ◽  
Common Noise ◽  
Finite State

A Starter: The First-Order Master Equation

2019 ◽  
pp. 48-84
Author(s):  
Pierre Cardaliaguet ◽  
François Delarue ◽  
Jean-Michel Lasry ◽  
Pierre-Louis Lions
Keyword(s):  
Master Equation ◽  
Preliminary Analysis ◽  
Initial Conditions ◽  
Mean Field ◽  
Mean Field Games ◽  
Lipschitz Continuous ◽  
First Order ◽  
Common Noise ◽  
The Mean ◽  
Uniformly Lipschitz

This chapter contains a preliminary analysis of the master equation in the simpler case when there is no common noise. Some of the proofs given in this chapter consist of a sketch only. One of the reasons is that some of the arguments used to investigate the mean field games (MFGs) system have been already developed in the literature. Another reason is that the chapter constitutes a starter only, specifically devoted to the simpler case without common noise. It provides details of the global Lipschitz continuity of H. The solutions of the MFG system are uniformly Lipschitz continuous, which are independently of initial conditions.

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

2019 ◽  
Author(s):  
Christoph Belak ◽  
Daniel Hoffmann ◽  
Frank Thomas Seifried
Keyword(s):  
State Space ◽  
Continuous Time ◽  
Mean Field ◽  
Mean Field Games ◽  
Common Noise ◽  
Finite State ◽  
Finite State Space

scholarly journals Finite state mean field games with Wright–Fisher common noise

2021 ◽  
Vol 147 ◽  
pp. 98-162
Author(s):  
Erhan Bayraktar ◽  
Alekos Cecchin ◽  
Asaf Cohen ◽  
François Delarue
Keyword(s):  
Mean Field ◽  
Mean Field Games ◽  
Common Noise ◽  
Finite State

The Second-Order Master Equation

2019 ◽  
pp. 128-158
Author(s):  
Pierre Cardaliaguet ◽  
François Delarue ◽  
Jean-Michel Lasry ◽  
Pierre-Louis Lions
Keyword(s):  
Master Equation ◽  
Mean Field ◽  
Second Order ◽  
Well Posedness ◽  
Mean Field Game ◽  
First Order ◽  
Common Noise ◽  
System P ◽  
The Mean

This chapter investigates the second-order master equation with common noise, which requires the well-posedness of the mean field game (MFG) system. It also defines and analyzes the solution of the master equation. The chapter explains the forward component of the MFG system that is recognized as the characteristics of the master equation. The regularity of the solution of the master equation is explored through the tangent process that solves the linearized MFG system. It also analyzes first-order differentiability and second-order differentiability in the direction of the measure on the same model as for the first-order derivatives. This chapter concludes with further description of the derivation of the master equation and well-posedness of the stochastic MFG system.

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
Sign in / Sign up

Export Citation Format

Share Document