Access the full text.
Sign up today, get DeepDyve free for 14 days.
Loading next page...
/lp/wiley/decentralized-epsilon-nash-strategy-for-linear-quadratic-mean-field-nCrijpHWkD
References (26)
-
A. Kizilkale, R. Salhab, R. Malhamé (2018)
An integral control formulation of Mean-field game based large scale coordination of loads in smart gridsArXiv, abs/1803.00040
-
A. Bensoussan, J. Frehse, Phillip Yam (2013)
Mean Field Games and Mean Field Type Control Theory -
Y. Achdou, M. Laurière (2020)
Mean field games and applications: numerical aspects, 2020
-
P. Cardaliaguet, Charles-Albert Lehalle (2016)
Mean field game of controls and an application to trade crowdingMathematics and Financial Economics, 12
-
P. Semasinghe, E. Hossain (2015)
Downlink power control in self?organizing dense small cells underlaying macrocells: a mean field game, 15
-
J. Lasry, P. Lions (2006)
Jeux à champ moyen. I – Le cas stationnaireComptes Rendus Mathematique, 343
-
Kai Du, Jianhui Huang, Zhen Wu (2018)
Linear quadratic mean-field-game of backward stochastic differential systemsMathematical Control and Related Fields, 8
-
J. Yong, X. Y. Zhou (1999)
Stochastic controls: Hamiltonian systems and HJB equations, 43
-
S. Cacace, F. Camilli, Alessandro Goffi (2020)
A policy iteration method for mean field gamesESAIM: Control, Optimisation and Calculus of Variations
-
R. Carmona, F. Delarue (2018)
Probabilistic Theory of Mean Field Games with Applications II: Mean Field Games with Common Noise and Master Equations -
M. Huang, P. E. Caines, R. P. Malhamé (2007)
Large?population cost?coupled LQG problems with nonuniform agents: individual?mass behavior and decentralized ??Nash equilibria, 52
-
M. Huang, J. H. Manton (2009)
Coordination and consensus of networked agents with noisy measurements: stochastic algorithms and asymptotic behavior, 48
-
Y. Hu, J. Huang, T. Nie (2018)
Linear?quadratic?Gaussian mixed mean?field games with heterogeneous input constraints, 56
-
Minyi Huang, Xuwei Yang (2021)
Linear Quadratic Mean Field Games: Decentralized O(1/N)-Nash EquilibriaJournal of Systems Science and Complexity, 34
-
M. Bardi (2012)
Explicit solutions of some linear-quadratic mean field gamesNetworks Heterog. Media, 7
-
M. Huang, R. P. Malhamé, P. E. Caines (2006)
Large population stochastic dynamic games: closed?loop McKean?Vlasov systems and the Nash certainty equivalence principle, 6
-
(1999)
Stochastic Controls -
O. Guéant, J.‐M. Lasry, P.‐L. Lions (2011)
Paris?Princeton lectures on mathematical finance 2010 -
J. Moon, T. Başar (2016)
Linear quadratic risk?sensitive and robust mean field games, 62
-
M. Huang, M. Zhou (2019)
Linear quadratic mean field games: asymptotic solvability and relation to the fixed point approach, 65
-
Bingchang Wang, Xin Yu, Hailing Dong (2020)
Social optima in linear quadratic mean field control with unmodeled dynamics and multiplicative noiseAsian Journal of Control, 23
-
Minyi Huang (2009)
Large-Population LQG Games Involving a Major Player: The Nash Certainty Equivalence PrincipleSIAM J. Control. Optim., 48
-
J. Lasry, P. Lions (2007)
Mean field gamesJapanese Journal of Mathematics, 2
-
D. Gomes, João Saúde (2014)
Mean Field Games Models—A Brief SurveyDynamic Games and Applications, 4
-
Kai Du, Zhen Wu (2022)
Social optima in mean field linear-quadratic-Gaussian models with control input constraintSyst. Control. Lett., 162
-
P. Cardaliaguet, Franccois Delarue, J. Lasry, P. Lions (2015)
The Master Equation and the Convergence Problem in Mean Field Games
- Publisher
- Wiley
- Copyright
- © 2023 Chinese Automatic Control Society and John Wiley & Sons Australia, Ltd
- ISSN
- 1561-8625
- eISSN
- 1934-6093
- DOI
- 10.1002/asjc.3085
- Publisher site
- See Article on Publisher Site
Abstract
This paper presents a successive approximation method for decentralized strategy design in the large‐scale linear quadratic (LQ) Gaussian game. The strategy consists of transforming the original mean field game (MFG) problem into solving decoupled ordinary differential equations (ODEs) whose numerical solutions are obtained by a new two‐loop iteration algorithm. It should be noted that we employ the augmented model technique and the LQ framework to derive these low‐dimensional solvable ODEs, which is the cornerstone of constructing the decentralized ϵ$$ \epsilon $$‐Nash strategy. In addition, the quadratic ODEs contained therein are approximately solved for by a sequence of iterative linear ordinary differential equations (LODEs) with guaranteed convergence. A numerical example is given to show the effectiveness of the proposed algorithm.
Journal
Asian Journal of Control – Wiley
Published: Apr 27, 2023
Keywords: augmented system; linear quadratic; mean field game; quadratic ordinary differential equations; successive approximation