Decentralized strategies for finite population linear-quadratic-Gaussian games and teams

卷:148

Article

关键词: MEAN-FIELD GAMES;    MULTIAGENT SYSTEMS;    MAJOR PLAYER;    NASH;    CONSENSUS;   

DOI  :  10.1016/j.automatica.2022.110789

来源: SCIE

【 摘 要 】

This paper is concerned with a new class of mean-field games which involve a finite number of agents. Necessary and sufficient conditions are obtained for the existence of the decentralized open-loop Nash equilibrium in terms of non-standard forward-backward stochastic differential equations (FBSDEs). By solving the FBSDEs, we design a set of decentralized strategies by virtue of two differential Riccati equations. Instead of the epsilon-Nash equilibrium in classical mean-field games, the set of decentralized strategies is shown to be a Nash equilibrium. For the infinite-horizon problem, a simple condition is given for the solvability of the algebraic Riccati equation arising from consensus. Furthermore, the social optimal control problem is studied. Under a mild condition, the decentralized social optimal control and the corresponding social cost are given. (c) 2022 Elsevier Ltd. All rights reserved.

【 授权许可】

Free