论文标题
在无限的地平线中
Mean-Field Linear-Quadratic Stochastic Differential Games in an Infinite Horizon
论文作者
论文摘要
本文与无限视野中的两人平均线性季度非零和随机差异游戏有关。引入了开环和闭环NASH平衡。开放环纳什平衡的存在的特征是，无限范围内的平均领域前向后随机微分方程的求解性以及成本函数的凸度，以及开放环nash平衡的闭环表示，通过两个方程式的溶液给出了两种不隔离的Alge Alge couplaimemmetermemmetermemmetrimemememmetramememememememmper的Alcat。闭环NASH平衡的存在的特征在于两个耦合对称代数riccati方程的系统的溶解度。还考虑了在无限时间范围内的两人平均线性季节零和随机差异游戏。开环和闭环鞍点的存在都以静态稳定溶液和静态稳定溶液的两个耦合通用代数riccati方程的系统的溶解度为特征。还讨论了无限视野中的平均场线性季节随机控制问题，为此证明，开环的溶解性和闭环可溶性是等效的。
This paper is concerned with two-person mean-field linear-quadratic non-zero sum stochastic differential games in an infinite horizon. Both open-loop and closed-loop Nash equilibria are introduced. Existence of an open-loop Nash equilibrium is characterized by the solvability of a system of mean-field forward-backward stochastic differential equations in an infinite horizon and the convexity of the cost functionals, and the closed-loop representation of an open-loop Nash equilibrium is given through the solution to a system of two coupled non-symmetric algebraic Riccati equations. The existence of a closed-loop Nash equilibrium is characterized by the solvability of a system of two coupled symmetric algebraic Riccati equations. Two-person mean-field linear-quadratic zero-sum stochastic differential games in an infinite time horizon are also considered. Both the existence of open-loop and closed-loop saddle points are characterized by the solvability of a system of two coupled generalized algebraic Riccati equations with static stabilizing solutions. Mean-field linear-quadratic stochastic optimal control problems in an infinite horizon are discussed as well, for which it is proved that the open-loop solvability and closed-loop solvability are equivalent.
