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 \n \Gamma \n of full space \n {\mathbb{R}}^{m}\n. 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 \n \Gamma \n. The wellposedness of consistency condition system is obtained using the monotonicity condition method. The related \n \in \n-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

^{1}; Huang, Jianhui

^{1}; Li, Xun

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@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}, publisher = {EDP-Sciences}, volume = {24}, number = {2}, year = {2018}, doi = {10.1051/cocv/2017038}, mrnumber = {3816421}, zbl = {1432.49048}, language = {en}, url = {http://archive.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 - http://archive.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 http://archive.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, Volume 24 (2018) no. 2, pp. 901-919. doi : 10.1051/cocv/2017038. http://archive.numdam.org/articles/10.1051/cocv/2017038/

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