Connections between mean-field game and social welfare optimization

Li，Sen1; Zhang，Wei2,3; Zhao，Lin3

2019-12-01

10.1016/j.automatica.2019.108590

AUTOMATICA   影响因子和分区

0005-1098

1873-2836

This paper studies the connection between a class of mean-field games and a social welfare optimization problem. We consider a mean-field game in function spaces with a large population of agents, and each agent seeks to minimize an individual cost function. The cost functions of different agents are coupled through a mean-field term that depends on the mean of the population states. We show that although the mean-field game is not a potential game, under some mild condition the ϵ-Nash equilibrium of the mean-field game coincides with the optimal solution to a modified social welfare optimization problem. This enables us to study the mean-field equilibrium using standard optimization theory. Based on this connection, we derive new results on the existence and uniqueness of the mean-field equilibrium. We also show that the mean-field equilibrium can be computed by a decentralized primal–dual algorithm. Numerical results are presented to validate the solution, and examples are provided to show the applicability of the proposed approach.

Mean-field game Optimization Pseudo-potential games

SCI ; EI ; SSCI

英语

通讯

National Science Foundation[CNS-1552838]

Automation & Control Systems ; Engineering

Automation & Control Systems ; Engineering, Electrical & Electronic

WOS:000495491900005

PERGAMON-ELSEVIER SCIENCE LTD

20194007486399

Optimization ; Site selection

Optimization Techniques:921.5

ENGINEERING

2-s2.0-85072699932

Scopus

1.Department of Mechanical EngineeringUniversity of California,Berkeley,United States
2.Department of Mechanical and Energy EngineeringSouthern University of Science and Technology,Shenzhen,China
3.Department of Electrical and Computer EngineeringThe Ohio State University,Columbus,United States

Li，Sen,Zhang，Wei,Zhao，Lin. Connections between mean-field game and social welfare optimization[J]. AUTOMATICA,2019,110.

Li，Sen,Zhang，Wei,&Zhao，Lin.(2019).Connections between mean-field game and social welfare optimization.AUTOMATICA,110.

Li，Sen,et al."Connections between mean-field game and social welfare optimization".AUTOMATICA 110(2019).