Decentralized Strategies for Finite Population Linear-Quadratic-Gaussian Games and Teams

Autor:	Wang, Bing-Chang, Zhang, Huanshui, Fu, Minyue, Liang, Yong
Rok vydání:	2022
Předmět:	Mathematics - Optimization and Control
Druh dokumentu:	Working Paper
Popis:	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 $\varepsilon$-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. Comment: 18 pages, 5 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2206.05754 Zobrazit plný text záznamu View this record from Arxiv