基于图形的网络演化博弈的拓扑结构

Topological structure of graph-based networked evolutionary games

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。

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.