scholarly journals A Fully Discrete Semi-Lagrangian Scheme for a First Order Mean Field Game Problem

2014 ◽  
Vol 52 (1) ◽  
pp. 45-67 ◽  
Author(s):  
E. Carlini ◽  
F. J. Silva
Keyword(s):  
Mean Field ◽  
Game Problem ◽  
Mean Field Game ◽  
First Order ◽  
Fully Discrete ◽  
Lagrangian Scheme

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 Viability analysis of the first-order mean field games

2020 ◽  
Vol 26 ◽  
pp. 33
Author(s):  
Yurii Averboukh
Keyword(s):  
Mean Field ◽  
Initial Distribution ◽  
Initial Time ◽  
Mean Field Games ◽  
Sufficient Condition ◽  
Mean Field Game ◽  
First Order ◽  
Viability Analysis ◽  
A Value ◽  
Object Of Study

In the paper, we examine the dependence of the solution of the deterministic mean field game on the initial distribution of players. The main object of study is the mapping which assigns to the initial time and the initial distribution of players the set of expected rewards of the representative player corresponding to solutions of mean field game. This mapping can be regarded as a value multifunction. We obtain the sufficient condition for a multifunction to be a value multifunction. It states that if a multifunction is viable with respect to the dynamics generated by the original mean field game, then it is a value multifunction. Furthermore, the infinitesimal variant of this condition is derived.

scholarly journals Obstacle mean-field game problem

2015 ◽  
Vol 17 (1) ◽  
pp. 55-68 ◽  
Author(s):  
Diogo Gomes ◽  
Stefania Patrizi
Keyword(s):  
Mean Field ◽  
Game Problem ◽  
Mean Field Game

scholarly journals Two-scale homogenization of a stationary mean-field game

2020 ◽  
Vol 26 ◽  
pp. 17
Author(s):  
Rita Ferreira ◽  
Diogo Gomes ◽  
Xianjin Yang
Keyword(s):  
Asymptotic Behavior ◽  
Existence And Uniqueness ◽  
Mean Field ◽  
Main Tool ◽  
Homogenization Theory ◽  
Mean Field Game ◽  
First Order ◽  
Limit Problems ◽  
Uniqueness Of The Solution ◽  
Oscillating Potential

In this paper, we characterize the asymptotic behavior of a first-order stationary mean-field game (MFG) with a logarithm coupling, a quadratic Hamiltonian, and a periodically oscillating potential. This study falls into the realm of the homogenization theory, and our main tool is the two-scale convergence. Using this convergence, we rigorously derive the two-scale homogenized and the homogenized MFG problems, which encode the so-called macroscopic or effective behavior of the original oscillating MFG. Moreover, we prove existence and uniqueness of the solution to these limit problems.

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