no. 2
Linear quadratic mean field game with control input constraint
ESAIM: Control, Optimisation and Calculus of Variations, Tome 24 (2018) no. 2, pp. 901-919.

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 ℝ m . 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 ∈ -Nash equilibrium property is also verified.

DOI : 10.1051/cocv/2017038
Classification : 60H10, 60H30, 91A10, 91A25, 93E20
Mots clés : 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

1 
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     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},
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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. http://www.numdam.org/articles/10.1051/cocv/2017038/

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