平均场对策与队的离散时间图的主方程
Master equation of discrete time graphon mean field games and teams
摘要：
本文提出了一种等价于Master方程的序列分解算法，用于计算GMFG的GMFE和图子平均场团队（GMFT）的图子最优马尔可夫策略（GOMP）。我们考虑了大量的球员顺序地作出战略决策，每个球员的行动影响他们的邻居，这是在一个图中捕获，由一个已知的graphon生成。每个局中人都观察到一个私有状态和一个公共信息，作为一个图子平均场种群状态，它代表了其他局中人类型的经验网络分布。我们考虑非平稳的人口状态动力学，并提出了一种新的向后递归算法来计算GMFE和GOMP，这取决于两个，玩家的私人类型，和当前（动态）人口状态确定通过graphon。计算GMFE的每一步都包括求解一个定点方程，而计算GOMP涉及求解一个优化问题。我们提供的条件，存在这样的GMFE的模型参数。使用该算法，我们获得了GMFE和GOMP的网络物理系统中的特定的安全设置为不同的图子，捕捉系统中的节点之间的相互作用。
英文摘要：
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.
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