In this paper, we present a sequential decomposition algorithm to compute graphon mean field equilibrium (GMFE) of dynamic graphon mean field game (GMFG). We consider a large population of players sequentially making strategic decisions where the actions of each player affect their neighbors which is captured in a graph, generated by a known graphon. Each player observes a private state and also a common information as a graphon mean-field population state which represents the empirical networked distribution of other players' types. We consider non-stationary population state dynamics and present a novel backward recursive algorithm to compute GMFE that depend on both, a player's private type, and the current (dynamic) population state determined through the graphon. Each step in this algorithm consists of solving a fixed-point equation. We provide conditions on model parameters for which there exists such a GMFE. Using this algorithm, we obtain the GMFE for a specific security setup in cyber physical systems for different graphons that capture the interactions between the nodes in the system.

中文翻译：

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Graphon 平均场博弈的顺序分解

在本文中，我们提出了一种顺序分解算法来计算动态图形平均场博弈（GMFG）的图形平均场平衡（GMFE）。我们考虑大量玩家依次做出战略决策，其中每个玩家的行为都会影响他们的邻居，该决策被捕获在由已知图形生成的图形中。每个玩家观察到一个私有状态和一个共同信息，作为一个代表其他玩家类型的经验网络分布的图子平均场人口状态。我们考虑了非平稳人口状态动态，并提出了一种新颖的后向递归算法来计算 GMFE，该算法取决于玩家的私人类型和通过图形确定的当前（动态）人口状态。该算法的每一步都包括求解一个定点方程。我们提供存在此类 GMFE 的模型参数的条件。使用该算法，我们获得了网络物理系统中特定安全设置的 GMFE，用于捕获系统中节点之间交互的不同图形。