Title :
Discrete-time mean field games in multi-agent systems
Author :
Xuehe Wang ; Nan Xiao ; Lihua Xie ; Frazzoli, Emilio ; Rus, Daniela
Author_Institution :
Sch. of Electr. & Electron. Eng., Nanyang Technol. Univ., Singapore, Singapore
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.
Keywords :
cost reduction; decentralised control; discrete time systems; game theory; multi-robot systems; optimal control; LTA cost; PSA; agent behavior; asymptotic Nash equilibrium; decentralized mean field control laws; decentralized mean field social control strategies; deterministic function; discrete-time mean field games; dynamic equation; infinite population systems; long time average cost; mean field Nash control; mean field term; mean-consensus; multiagent systems; optimal control; population state average; social cost minimization; socially optimal case; Approximation methods; Cost function; Decentralized control; Games; Optimal control; Sociology; Statistics;
Conference_Titel :
Control Automation Robotics & Vision (ICARCV), 2014 13th International Conference on
DOI :
10.1109/ICARCV.2014.7064391