论文标题
有限人口线性 - 季度高斯游戏和团队的分散策略
Decentralized Strategies for Finite Population Linear-Quadratic-Gaussian Games and Teams
论文作者
论文摘要
本文关注的是一类新的平均场游戏，涉及有限的代理商。对于非标准前向后的随机微分方程（FBSDES）而言，获得了分散的开环NASH平衡的必要条件。通过解决FBSDE，我们通过两个差异riccati方程设计了一套分散策略。与代替$ \ varepsilon $ -NASH在经典均值游戏中的平衡，一组分散的策略被证明是NASH平衡。对于无限 - 水平问题，为代数riccati方程的可溶性提供了简单的条件。此外，还研究了社会最佳控制问题。在温和的情况下，给出了分散的社会最佳控制和相应的社会成本。
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.
