- Title
- Decentralized strategies for finite population linear–quadratic–Gaussian games and teams
- Creator
- Wang, Bing-Chang; Zhang, Huanshui; Fu, Minyue; Liang, Yong
- Relation
- ARC.DP200103507 http://purl.org/au-research/grants/arc/DP200103507
- Relation
- Automatica Vol. 148, Issue February 2023, no. 110789
- Publisher Link
- http://dx.doi.org/10.1016/j.automatica.2022.110789
- Publisher
- Elsevier
- Resource Type
- journal article
- Date
- 2023
- Description
- 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 ɛ-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.
- Subject
- mean-field game; decentralized nash equilibrium; finite population; non-standard FBSDE; weighted cost
- Identifier
- http://hdl.handle.net/1959.13/1477888
- Identifier
- uon:50051
- Identifier
- ISSN:0005-1098
- Language
- eng
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