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 of full space . 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 . The wellposedness of consistency condition system is obtained using the monotonicity condition method. The related -Nash equilibrium property is also verified.
Keywords: ϵ-Nash equilibrium, mean-field forward-backward stochastic differential equation (MF-FBSDE), linear-quadratic constrained control, projection, monotonic condition
Hu, Ying 1 ; Huang, Jianhui 1 ; Li, Xun 1
@article{COCV_2018__24_2_901_0,
author = {Hu, Ying and Huang, Jianhui and Li, Xun},
title = {Linear quadratic mean field game with control input constraint},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {901--919},
year = {2018},
publisher = {EDP Sciences},
volume = {24},
number = {2},
doi = {10.1051/cocv/2017038},
mrnumber = {3816421},
zbl = {1432.49048},
language = {en},
url = {https://www.numdam.org/articles/10.1051/cocv/2017038/}
}
TY - JOUR AU - Hu, Ying AU - Huang, Jianhui AU - Li, Xun TI - Linear quadratic mean field game with control input constraint JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2018 SP - 901 EP - 919 VL - 24 IS - 2 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/cocv/2017038/ DO - 10.1051/cocv/2017038 LA - en ID - COCV_2018__24_2_901_0 ER -
%0 Journal Article %A Hu, Ying %A Huang, Jianhui %A Li, Xun %T Linear quadratic mean field game with control input constraint %J ESAIM: Control, Optimisation and Calculus of Variations %D 2018 %P 901-919 %V 24 %N 2 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/cocv/2017038/ %R 10.1051/cocv/2017038 %G en %F COCV_2018__24_2_901_0
Hu, Ying; Huang, Jianhui; Li, Xun. Linear quadratic mean field game with control input constraint. ESAIM: Control, Optimisation and Calculus of Variations, Tome 24 (2018) no. 2, pp. 901-919. doi: 10.1051/cocv/2017038
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