| Issue |
ESAIM: COCV
Volume 24, Number 2, April–June 2018
|
|
|---|---|---|
| Page(s) | 901 - 919 | |
| DOI | https://doi.org/10.1051/cocv/2017038 | |
| Published online | 13 June 2018 | |
Linear quadratic mean field game with control input constraint★
1
IRMAR, Université Rennes 1, Campus de Beaulieu,
35042
Rennes Cedex, France
2
Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong
majhuang@polyu.edu.hk; malixun@polyu.edu.hk
a Corresponding author: ying.hu@univ-rennes1.fr
Received:
21
October
2016
Revised:
10
March
2017
Accepted:
11
May
2017
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.
Mathematics Subject Classification: 60H10 / 60H30 / 91A10 / 91A25 / 93E20
Key words: ϵ-Nash equilibrium / mean-field forward-backward stochastic differential equation (MF-FBSDE) / linear-quadratic constrained control / projection / monotonic condition
The work of Ying Hu is supported by Lebesgue center of mathematics “Investissements d'avenir” program - ANR-11-LABX-0020-01, by ANR-15-CE05-0024 and by ANR-16-CE40-0015-01; The work of James Jianhui Huang is supported by PolyU G-YL04, RGC Grant 502412, 15300514; The work of Xun Li is supported by PolyU G-UA4N, Hong Kong RGC under grants 15224215 and 15255416.
© EDP Sciences, SMAI 2018
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