In this paper, we present a sequential decomposition algorithm equivalent of Master equation to compute GMFE of GMFG and graphon optimal Markovian policies (GOMPs) of graphon mean field teams (GMFTs). 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 both GMFE and GOMP that depend on both, a player's private type, and the current (dynamic) population state determined through the graphon. Each step in computing GMFE consists of solving a fixed-point equation, while computing GOMP involves solving for an optimization problem. We provide conditions on model parameters for which there exists such a GMFE. Using this algorithm, we obtain the GMFE and GOMP for a specific security setup in cyber physical systems for different graphons that capture the interactions between the nodes in the system.

翻译：在本文中,我们展示了相当于主方程式的连续分解算法,以计算GMFG和Ggonon平均战地小组的GNOPPE最佳Markovian政策(GOMPs)的GMEFE。我们认为,有大量的玩家按顺序做出战略决定,其中每个玩家的行动会影响其邻居,通过已知的图解绘制出来。每个玩家观察一个私人状态,并作为代表其他玩家类型实验网络分布的图示平均场人口状态的普通信息。我们考虑了非静止人口动态,并提出了一种新的后向回溯递算法,既取决于玩家的私人类型,又取决于通过图形决定的当前(动态)人口状况。计算GMEFE的每一个步骤是解决固定点方程式,而计算GOMP则涉及解决优化问题。我们为存在这种GMEFE的模型参数提供了条件。我们利用这一算法,获得了GMEFE和GOMP在网络物理系统中为不同图形系统设置的具体安全设置,以捕捉取系统中的节点之间的相互作用。