Paper Info
Title
Discrete-time mean field games in multi-agent systems
Abstract
In this paper, we investigate the behavior of agents in mean field games where each agent evolves according to a dynamic equation containing the input average and seeks to minimize its long time average (LTA) cost encompassing a population state average (PSA), which is also known as the mean field term. Due to the informational burden resulting from the PSA coupling to the states of all agents, our idea is to find a deterministic function φ to approximate it. It is shown that φ is an approximation of the PSA as the population size N goes to infinity. The resulting decentralized mean field control laws lead the system to achieve mean-consensus asymptotically as time goes to infinity. Furthermore, the optimal controls generate an almost sure asymptotic Nash equilibrium, which implies that the LTA cost of each agent can reach its minimal value as the number of agents increases to infinity. Finally, we consider the socially optimal case where the basic objective is to minimize the social cost as the sum of the individual LTA cost containing the PSA. In this case, it is shown that the decentralized mean field social control strategies are the same as the mean field Nash controls for infinite population systems.
Year
DOI
Venue
2014
10.1109/ICARCV.2014.7064391
ICARCV
Keywords
Field
DocType
mean field nash control,optimal control,psa,population state average,infinite population systems,mean-consensus,mean field term,multi-robot systems,discrete-time mean field games,long time average cost,game theory,lta cost,deterministic function,asymptotic nash equilibrium,socially optimal case,social cost minimization,discrete time systems,multiagent systems,decentralized mean field control laws,decentralized mean field social control strategies,agent behavior,decentralised control,cost reduction,dynamic equation,sociology,games,decentralized control,statistics,cost function
Population,Mathematical optimization,Decentralised system,Optimal control,Computer science,Control theory,Infinity,Multi-agent system,Mean field theory,Discrete time and continuous time,Nash equilibrium
Conference
ISSN
Citations 
PageRank 
2474-2953
1
0.36
References 
Authors
8
5
Name
Order
Citations
PageRank
Xuehe Wang1164.11
Nan Xiao2345.97
Lihua Xie35686405.63
Emilio Frazzoli43286229.95
Daniela Rus57128657.33