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.
Mots-clés : ϵ-Nash equilibrium, mean-field forward-backward stochastic differential equation (MF-FBSDE), linear-quadratic constrained control, projection, monotonic condition
@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, Tome 24 (2018) no. 2, pp. 901-919. doi : 10.1051/cocv/2017038. http://archive.numdam.org/articles/10.1051/cocv/2017038/
[1] Appl. Funct. Anal. Springer–Verlag, New York (1976) | MR
,[2] Mean Field Games and Mean Field Type Control Theory. Springer, New York (2013) | DOI | MR | Zbl
, and ,[3] Functional Analysis, Sobolev Spaces Partial Differ. Equ. Springer, New York (2011) | MR | Zbl
,[4] Notes on Mean Field Games (2012)
,[5] Probabilistic analysis of mean-field games. SIAM J. Control Optim. 51 (2013) 2705–2734 | DOI | MR | Zbl
and ,[6] Mean field games and systemic risk. Commun. Math. Sci. 13 (2015) 911–933 | DOI | MR | Zbl
, and ,[7] Optimal investment under relative performance concerns. Math. Finance 25 (2015) 221–257 | DOI | MR | Zbl
and ,[8] Mean field games and applications. Paris-Princeton Lectures on Mathematical Finance 2010 Lect. Notes Math. 2011 205–266 | MR | Zbl
, and ,[9] Constrained stochastic LQ control with random coefficients, and application to portfolio selection. SIAM J. Control Optim. 44 (2005) 444–466 | DOI | MR | Zbl
and ,[10] Solutions of forward-backward stochastic differential equations. Prob. Theory Related Fields 103 (1995) 273–283 | DOI | MR | Zbl
and ,[11] Large population LQG games involving a major player: The Nash certainty equivalence principle. SIAM J. Control Optim. 48 (2010) 3318–3353 | DOI | MR | Zbl
,[12] Distributed multi-agent decision-making with partial observations: Asymptotic Nash equilibria. Proceedings of the 17th Int. Symp. Math. Theory Networks Syst. Kyoto, Japan (2006)
, and ,[13] Large-population cost-coupled LQG problems with non-uniform agents: Individual-mass behavior and decentralized ε-Nash equilibria. IEEE Trans. Automat. Control 52 (2007) 1560–1571 | DOI | MR | Zbl
, and ,[14] Large population stochastic dynamic games: closed-loop McKean-Vlasov systems and the Nash certainty equivalence principle. Commun. Infor. Syst. 6 (2006) 221–251 | DOI | MR | Zbl
, and ,[15] Mean field games. Jpn J. Math. 2 (2007) 229–260 | DOI | MR | Zbl
and ,[16] Linear-quadratic-Gaussian mixed games with continuum-parameterized minor players. SIAM J. Control Optim. 50 (2012) 2907–2937 | DOI | MR | Zbl
and ,[17] Fully coupled forward-backward stochastic differential equations and applications to optimal control. SIAM J. Control Optim. 37 (1999) 825–843 | DOI | MR | Zbl
and ,[18] Risk-sensitive mean-field games. IEEE Trans. Automat. Control 59 (2014) 835–850 | DOI | MR | Zbl
, and ,[19] Mean field games for large-population multiagent systems with Markov jump parameters. SIAM J. Control Optim. 50 (2012) 2308–2334 | DOI | MR | Zbl
and ,[20] Linear-quadratic optimal control problem for mean-field stochastic differential equations. SIAM J. Control Optim. 51 (2013) 2809–2838 | DOI | MR | Zbl
,[21] Stochastic controls: Hamiltonian systems and HJB equations. Springer–Verlag, New York (1999) | DOI | MR | Zbl
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