Name
Abstract | ||
|---|---|---|
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. |
Year | DOI | Venue |
|---|---|---|
2019 | 10.1016/j.automatica.2019.108590 | Automatica |
Keywords | Field | DocType |
Mean-field game,Optimization,Pseudo-potential games | Population,Uniqueness,Mathematical optimization,Function space,Potential game,Regular polygon,Optimization problem,Mathematics,Social Welfare,Computation | Journal |
Volume | Issue | ISSN |
110 | 1 | 0005-1098 |
Citations | PageRank | References |
1 | 0.34 | 7 |
Authors | ||
3 | ||