扩展平均场控制博弈与矩交互：一般框架与线性二次模型
Extended Mean Field Control Games with Moment Interactions: General Framework and Linear-Quadratic Model
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中文总结 AI 辅助
本文提出扩展平均场控制博弈的一般框架，通过动作均值引入交互，并在线性二次结构下将均衡简化为常微分方程组，推广了平均场博弈与平均场控制的结果。
中文摘要 AI 辅助
平均场控制博弈（MFCGs）提供了一个框架，用于研究在玩家数量和群体数量均趋于无穷大的极限情况下，涉及多个合作玩家群体的非合作博弈。这类博弈将平均场博弈（MFGs）和平均场控制（MFC）问题作为特例，分别对应纯粹非合作和纯粹合作的情形。我们通过动作的均值引入交互，因此称之为扩展MFCGs。我们首先证明，均衡控制可以用一个由Hamilton-Jacobi-Bellman方程和Fokker-Planck方程组成的偏微分方程耦合系统来描述。在引入一般框架之后，我们聚焦于线性二次（LQ）结构。我们证明，均衡可以归结为一个常微分方程组，该方程组推广了为MFGs和MFC问题所得到的方程组。最后，我们提供两个数值示例，以说明MFCGs的特定特征。
英文摘要
Mean field control games (MFCGs) provide a framework for studying non-cooperative games involving groups of cooperative players in the limit as both the number of players and the number of groups go to infinity.This class of games includes mean field games (MFGs) and mean field control (MFC) problems as special cases, corresponding to purely non-cooperative and purely cooperative settings, respectively. We incorporate interactions through the mean of actions, hence the terminology of extended MFCGs. We first show that the equilibrium control can be described using a coupled system of partial differential equations consisting of a Hamilton-Jacobi-Bellman equation and a Fokker-Planck equation. After introducing the general framework, we focus on a linear-quadratic (LQ) structure. We show that the equilibrium can be reduced to a system of ODEs, generalizing those obtained for MFGs and MFC problems. We then provide two numerical examples illustrating specific features of MFCGs.
发表机构
- NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai（纽约大学-华东师范大学上海数学中心）
机构由 AI 辅助整理，请以论文原文为准。
