An Alternative Approach to Mean Field Game with Major and Minor Players, and Applications to Herders Impacts

被引:23
作者
Carmona, Rene [1 ]
Wang, Peiqi [1 ]
机构
[1] Princeton Univ, Dept Operat Res & Financial Engn, Princeton, NJ 08544 USA
基金
美国国家科学基金会;
关键词
D O I
10.1007/s00245-017-9430-4
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
The goal of the paper is to introduce a formulation of the mean field game with major and minor players as a fixed point on a space of controls. This approach emphasizes naturally the role played by McKean-Vlasov dynamics in some of the players' optimization problems. We apply this approach to linear quadratic models for which we recover the existing solutions for open loop equilibria, and we show that we can also provide solutions for closed loop versions of the game. Finally, we implement numerically our theoretical results on a simple model of flocking.
引用
收藏
页码:5 / 27
页数:23
相关论文
共 11 条
[1]  
Bensoussan A., 2013, TECH REP, DOI [10.1007/s00245-015-9309-1, DOI 10.1007/S00245-015-9309-1]
[2]  
Carmona R., 2017, PROBABILISTIC THEORY, VI-II
[3]  
Carmona R., 2017, PROBABILISTIC THEORY, VII
[4]   A PROBABILISTIC APPROACH TO MEAN FIELD GAMES WITH MAJOR AND MINOR PLAYERS [J].
Carmona, Rene ;
Zhu, Xiuneng .
ANNALS OF APPLIED PROBABILITY, 2016, 26 (03) :1535-1580
[5]   Emergent behavior in flocks [J].
Cucker, Felipe ;
Smale, Steve .
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2007, 52 (05) :852-862
[6]   LARGE-POPULATION LQG GAMES INVOLVING A MAJOR PLAYER: THE NASH CERTAINTY EQUIVALENCE PRINCIPLE [J].
Huang, Minyi .
SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2010, 48 (05) :3318-3353
[7]  
Jaimungal S., 2015, TECH REP
[8]  
Nguyen S., 2015, SIAM J CONTROL OPTIM, V50, P2907
[9]  
Nguyen S.L., 2012, 51 IEEE C DEC CONTR
[10]  
Nourian M., 2011, P 18 IFAC WORLD C MI, P4471