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

scholarly journals Linear quadratic mean field game with control input constraint

2018 ◽  
Vol 24 (2) ◽  
pp. 901-919 ◽  
Author(s):  
Ying Hu ◽  
Jianhui Huang ◽  
Xun Li
Keyword(s):  
Backward Stochastic Differential Equation ◽  
Consistency Condition ◽  
Mean Field ◽  
Control Process ◽  
Mean Field Games ◽  
Monotonicity Condition ◽  
Projection Operators ◽  
Control Input ◽  
Linear Quadratic ◽  
The Individual

In this paper, we study a class of linear-quadratic (LQ) mean-field games in which the individual control process is constrained in a closed convex subset Γ of full space ℝm. The decentralized strategies and consistency condition are represented by a class of mean-field forward-backward stochastic differential equation (MF-FBSDE) with projection operators on Γ. The wellposedness of consistency condition system is obtained using the monotonicity condition method. The related ϵ-Nash equilibrium property is also verified.

scholarly journals Linear-Quadratic Mean Field Games

2015 ◽  
Vol 169 (2) ◽  
pp. 496-529 ◽  
Author(s):  
A. Bensoussan ◽  
K. C. J. Sung ◽  
S. C. P. Yam ◽  
S. P. Yung
Keyword(s):  
Mean Field ◽  
Mean Field Games ◽  
Linear Quadratic ◽  
Quadratic Mean

scholarly journals Price of anarchy for Mean Field Games

2019 ◽  
Vol 65 ◽  
pp. 349-383 ◽  
Author(s):  
René Carmona ◽  
Christy V. Graves ◽  
Zongjun Tan
Keyword(s):  
Social Cost ◽  
Price Of Anarchy ◽  
Mean Field ◽  
Mean Field Games ◽  
Necessary Condition ◽  
Linear Quadratic ◽  
Selfish Behavior ◽  
Worst Case ◽  
Game Equilibrium ◽  
Routing Games

The price of anarchy, originally introduced to quantify the inefficiency of selfish behavior in routing games, is extended to mean field games. The price of anarchy is defined as the ratio of a worst case social cost computed for a mean field game equilibrium to the optimal social cost as computed by a central planner. We illustrate properties of such a price of anarchy on linear quadratic extended mean field games, for which explicit computations are possible. A sufficient and necessary condition to have no price of anarchy is presented. Various asymptotic behaviors of the price of anarchy are proved for limiting behaviors of the coefficients in the model and numerics are presented.

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