大规模网络上的异步半匿名动力学
Asynchronous semi-anonymous dynamics over large-scale networks
摘要：
我们分析了一类随机过程，称为异步和半匿名动力学（ASD），在有向标记随机网络。这些过程是一个自然的工具来描述一般的最佳反应和嘈杂的最佳反应动态网络游戏中，每个代理，在随机时间由独立的泊松时钟，可以选择一组有限的行动。收益由邻居之间不同行为的相对流行度决定，而与邻居的具体身份无关。使用平均场的方法，我们证明了，在一定的条件下的网络和初始节点配置，ASD的演变可以近似，在大的网络尺寸的限制，由一个系统的非线性常微分方程的解决方案。我们的框架是非常普遍的，并适用于一个大类的图形集成，典型的随机图局部表现得像一棵树。特别是，我们将专注于标记的配置模型随机图，传统的配置模型的推广，允许不同类别的节点在网络中混合在一起，允许我们，例如，在系统中纳入社区结构。我们的分析也适用于具有幂律度分布的配置模型图，这是许多真实系统的基本特征。为了证明我们的框架的力量和灵活性，我们考虑几个例子属于我们的随机过程类的动态。此外，我们通过模拟来说明我们的分析在现实场景中的适用性，通过在真实的社交网络图上运行我们的示例动态。
英文摘要：
We analyze a class of stochastic processes, referred to as asynchronous and semi-anonymous dynamics (ASD), over directed labeled random networks. These processes are a natural tool to describe general best-response and noisy best-response dynamics in network games where each agent, at random times governed by independent Poisson clocks, can choose among a finite set of actions. The payoff is determined by the relative popularity of different actions among neighbors, while being independent of the specific identities of neighbors. Using a mean-field approach, we prove that, under certain conditions on the network and initial node configuration, the evolution of ASD can be approximated, in the limit of large network sizes, by the solution of a system of non-linear ordinary differential equations. Our framework is very general and applies to a large class of graph ensembles for which the typical random graph locally behaves like a tree. In particular, we will focus on labeled configuration-model random graphs, a generalization of the traditional configuration model which allows different classes of nodes to be mixed together in the network, permitting us, for example, to incorporate a community structure in the system. Our analysis also applies to configuration-model graphs having a power-law degree distribution, an essential feature of many real systems. To demonstrate the power and flexibility of our framework, we consider several examples of dynamics belonging to our class of stochastic processes. Moreover, we illustrate by simulation the applicability of our analysis to realistic scenarios by running our example dynamics over a real social network graph.
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