论文标题
部分可观测时空混沌系统的无模型预测
Mean Field Games with Major and Minor Agents: the Limiting Problem and Nash Equilibrium
论文作者
论文摘要
在本文中，我们考虑了一款具有专业和$ n $ binor代理商的平均现场游戏（MFG）。我们首先考虑限制问题，并允许系数以非线性方式随条件分布而变化。我们使用随机最大原理将限制控制问题转换为两个耦合条件分布的系统，依赖于前向后的随机微分方程（FBSDES），并证明当主要药物和次要药物之间的依赖性足够弱时，FBSDE的存在和唯一性产生。然后，我们使用限制问题的解决方案来构建$ \ Mathcal {o}（n^{ - \ frac {1} {2}}}}）$ - NASH平衡，用于MFG，具有主要和$ n $ n $ binor代理。
In this paper, we consider a mean field game (MFG) with a major and $N$ minor agents. We first consider the limiting problem and allow the coefficients to vary with the conditional distribution in a nonlinear way. We use the stochastic maximum principle to transform the limiting control problem into a system of two coupled conditional distribution dependent forward-backward stochastic differential equations (FBSDEs), and prove the existence and uniqueness result of the FBSDEs when the dependence between major agent and minor agents is sufficiently weak. We then use the solution of the limiting problem to construct an $\mathcal{O}(N^{-\frac{1}{2}})$-Nash equilibrium for the MFG with a major and $N$ minor agents.
