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The three kinds of degree distributions and nash equilibrium on the limiting random network
Stochastics and Dynamics ( IF 1.1 ) Pub Date : 2019-12-30 , DOI: 10.1142/s0219493720500331
Dong Han 1 , Min Xia 1
Affiliation  

A generalized dynamically evolving random network and a game model taking place on the evolving network are presented. We show that there exists a high-dimensional critical curved surface of the parameters related the probabilities of adding or removing vertices or edges such that the evolving network may exhibit three kinds of degree distributions as the time goes to infinity when the parameters belong to the super-critical, critical and sub-critical curved surfaces, respectively. Some sufficient conditions are given for the existence of a regular Nash equilibrium which depends on the three kinds of degree distributions in the game model on the limiting random network.

中文翻译:

有限随机网络上的三种度分布与纳什均衡

提出了一个广义的动态演化随机网络和一个发生在演化网络上的博弈模型。我们证明了存在与添加或删除顶点或边的概率相关的参数的高维临界曲面,使得当参数属于超级时,随着时间趋于无穷大,演化的网络可能表现出三种度数分布- 分别为临界、临界和亚临界曲面。给出了依赖于有限随机网络博弈模型中三种度分布的正则纳什均衡存在的充分条件。
更新日期:2019-12-30
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