Linear quadratic mean field game with control input constraint

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 d...

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Published inESAIM. Control, optimisation and calculus of variations Vol. 24; no. 2; pp. 901 - 919
Main Authors Hu, Ying, Huang, Jianhui, Li, Xun
Format Journal Article
LanguageEnglish
Published Les Ulis EDP Sciences 01.04.2018
Subjects
60H10
60H30
91A10
91A25
93E20
Consistency
Differential equations
Game theory
linear-quadratic constrained control
Mathematics
mean-field forward-backward stochastic differential equation (MF-FBSDE)
monotonic condition
Optimization and Control
Probability
projection
ϵ-Nash equilibrium
ǫ-Nash equilibrium
Monotonic condition
Linear-quadratic constrained control
60H10
Projection
Mean-field forward-backward stochastic differential equa
AMS Subject Classification: 93E20
tion (MF-FBSDE)
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Summary: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.
Bibliography:majhuang@polyu.edu.hk; malixun@polyu.edu.hk
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.
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ISSN:1292-8119
1262-3377
DOI:10.1051/cocv/2017038