基于图形的网络演化博弈的拓扑结构

doi:10.6040/j.issn.1671-9352.9.2021.001

《山东大学学报(理学版)》 ›› 2021, Vol. 56 ›› Issue (10): 11-22.doi: 10.6040/j.issn.1671-9352.9.2021.001

基于图形的网络演化博弈的拓扑结构

程代展

中国科学院数学与系统科学研究院, 系统控制重点实验室, 北京 100190

出版日期:2021-10-20 发布日期:2021-09-28
作者简介:CHENG Dai-zhan(1946— ), Male, Professor, Research Interests： nonlinear control system theory. E-mail:dcheng@iss.ac.cn

Topological structure of graphbased networked evolutionary games

CHENG Dai-zhan

Institute of Systems Science, Chinese Academy of Sciences, Beijing 100190, China

Online:2021-10-20 Published:2021-09-28

摘要/Abstract

摘要： 对基于图形的网络演化博弈,首先求出典型结点策略演化方程,进而给出将结点方程组合成网络局势演化方程的方法。利用局势演化方程,将计算逻辑动态系统不动点与极限环的公式推广用于图形的网络演化博弈。然后,介绍某玩家单独更新的局势演化方程,并依此给出网络演化博弈纯纳什均衡点计算公式。

关键词: 网络演化博弈, 局势演化方程, 单独更新的局势(演化)方程, 纯纳什均衡, 矩阵半张量积

Abstract: For a graph-based networked evolutionary game, the strategy evolutional equations for typical nodes are first calculated. A method is proposed to assemble typical node equations together to form the profile evolutional equation. The formula for calculating fixed points and limit cycles of logical networks is applicable to reveal the topological structure of networked evolutionary games, including the fixed points and limit cycles of networked evolutionary games. Next, for each player the unilateral profile updating equation is introduced. Using them, a formula for calculating pure Nash equilibrium(s)is obtained. Some numerical examples are presented.

Key words: networked evolutionary game, profile dynamic equation, unilateral profile updating equation, pure Nash equilibrium, semi-tensor product of matrices

中图分类号:

B815.2

程代展. 基于图形的网络演化博弈的拓扑结构[J]. 《山东大学学报(理学版)》, 2021, 56(10): 11-22.

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基于图形的网络演化博弈的拓扑结构

Topological structure of graphbased networked evolutionary games

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