scholarly journals On the convergence of closed-loop Nash equilibria to the mean field game limit

2020 ◽  
Vol 30 (4) ◽  
pp. 1693-1761 ◽  
Author(s):  
Daniel Lacker
Keyword(s):  
Nash Equilibria ◽  
Closed Loop ◽  
Mean Field ◽  
Mean Field Game ◽  
The Mean

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 Schrödinger approach to Mean Field Games with negative coordination

2020 ◽  
Vol 9 (4) ◽  
Author(s):  
Thibault Bonnemain ◽  
Thierry Gobron ◽  
Denis Ullmo
Keyword(s):  
Mean Field ◽  
Time Limit ◽  
External Potential ◽  
Mean Field Games ◽  
Relative Importance ◽  
Mean Field Game ◽  
Non Linear ◽  
The Mean ◽  
The Way

Mean Field Games provide a powerful framework to analyze the dynamics of a large number of controlled agents in interaction. Here we consider such systems when the interactions between agents result in a negative coordination and analyze the behavior of the associated system of coupled PDEs using the now well established correspondence with the non linear Schrödinger equation. We focus on the long optimization time limit and on configurations such that the game we consider goes through different regimes in which the relative importance of disorder, interactions between agents and external potential vary, which makes possible to get insights on the role of the forward-backward structure of the Mean Field Game equations in relation with the way these various regimes are connected.

scholarly journals Convergence to the mean field game limit: A case study

2020 ◽  
Vol 30 (1) ◽  
pp. 259-286 ◽  
Author(s):  
Marcel Nutz ◽  
Jaime San Martin ◽  
Xiaowei Tan
Keyword(s):  
Mean Field ◽  
Mean Field Game ◽  
The Mean

scholarly journals Learning in mean field games: The fictitious play

2017 ◽  
Vol 23 (2) ◽  
pp. 569-591 ◽  
Author(s):  
Pierre Cardaliaguet ◽  
Saeed Hadikhanloo
Keyword(s):  
Differential Games ◽  
Mean Field ◽  
Mean Field Games ◽  
Fictitious Play ◽  
Mean Field Game ◽  
Interacting Agents ◽  
Learning Procedure ◽  
Equilibrium Configurations ◽  
The Mean

Mean Field Game systems describe equilibrium configurations in differential games with infinitely many infinitesimal interacting agents. We introduce a learning procedure (similar to the Fictitious Play) for these games and show its convergence when the Mean Field Game is potential.

Presentation of the Main Results

2019 ◽  
pp. 28-47
Author(s):  
Pierre Cardaliaguet ◽  
François Delarue ◽  
Jean-Michel Lasry ◽  
Pierre-Louis Lions
Keyword(s):  
Master Equation ◽  
Classical Solution ◽  
Mean Field ◽  
Approximate Solutions ◽  
Unique Classical Solution ◽  
Mean Field Game ◽  
The Mean ◽  
Derivatives Of

This chapter collects the main results of the master equation for the convergence of the Nash system. It explains the notation used, specifies the notion of derivatives in the space of measures, and describes the assumptions on the data. One of the striking features of the master equation is that it involves derivatives of the unknown with respect to the measure. This chapter also discusses the link between the two notions of derivatives, which have been used in the mean field game (MFG) theory. The main result states that the master equation has a unique classical solution under the regularity and monotonicity assumptions on H, F, and G. Once the master equation has a solution, this solution can be used to build approximate solutions for the Nash system with N-players.

scholarly journals Optimal defense strategy based on the mean field game model for cyber security

2019 ◽  
Vol 15 (2) ◽  
pp. 155014771983118
Author(s):  
Li Miao ◽  
Lina Wang ◽  
Shuai Li ◽  
Haitao Xu ◽  
Xianwei Zhou
Keyword(s):  
Cyber Security ◽  
Mean Field ◽  
Game Model ◽  
Optimal Defense ◽  
Mean Field Game ◽  
Defense Strategy ◽  
The Mean
Sign in / Sign up

Export Citation Format

Share Document