NDLI: Decentralised dynamic games for large population stochastic multi-agent systems

Content Provider	IET Digital Library
Author	Wang, Xuehe Xiao, Nan Xie, Lihua Frazzoli, Emilio Rus, Daniela
Abstract	In this study, the authors consider the large population dynamic games where each agent evolves according to a dynamic equation containing the input average of all agents. The long time average (LTA) cost that each agent aims to minimise is coupled with other agents’ states via a population state average (PSA), which is also known as the mean field term. In order to design decentralised controls, the Nash certainty equivalence is introduced. It is shown that the resulting decentralised mean field control laws lead the system to mean-consensus asymptotically as time goes to infinity. The stability property of the mass behaviour and the almost sure asymptotic Nash equilibrium property of the optimal controls are also guaranteed, and the case with non-linear system dynamics is also discussed. In addition, the influence of inaccurate mean field information on individual agent is analysed. Finally, they investigate the socially cooperative formulation where the objective is to minimise the social cost as the sum of all individual LTA costs containing the PSA. In this case, they show that the decentralised mean field social controls are the same as the mean field Nash controls for infinite population systems.
Starting Page	503
Ending Page	510
Page Count	8
ISSN	17518644
Volume Number	9
e-ISSN	17518652
Issue Number	Issue 3, Feb (2015)
Alternate Webpage(s)	https://digital-library.theiet.org/content/journals/iet-cta/9/3
Alternate Webpage(s)	https://digital-library.theiet.org/content/journals/10.1049/iet-cta.2014.0625
Journal	IET Control Theory & Applications
Publisher Date	2014-12-19
Access Restriction	Open
Rights Holder	© The Institution of Engineering and Technology
Subject Keyword	Agent States Artificial Intelligence Asymptotic Nash Equilibrium Property Asymptotic Stability Decentralised Control Decentralised Control Design Decentralised Dynamic Games Decentralised Mean Field Social Control Law Dynamic Equation Game Theory Infinite Population System Long Time Average Cost LTA Cost Mass Behaviour Mean Field Nash Control Multi-agent System Multivariable Control System Nash Certainty Equivalence Nonlinear Control System Nonlinear Dynamical System Nonlinear System Dynamics Optimal Control Population State Average Population Stochastic Multiagent System PSA Stability in Control Theory Stability Property Stochastic System Time Varying Control System
Content Type	Text
Resource Type	Article
Subject	Control and Optimization Control and Systems Engineering Human-Computer Interaction Electrical and Electronic Engineering Computer Science Applications

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