论文标题
在网络上进化游戏中的普遍性汉密尔顿动态和混乱
Generalized Hamiltonian Dynamics and Chaos in Evolutionary Games on Networks
论文作者
论文摘要
我们研究网络复制器方程，并以$ 2 \ times 2 $对称游戏为单位上的固定点。我们展示了网络复制器的渐近行为与图中设置的独立顶点的存在之间的关系，还表明复杂的行为不能以$ 2 \ times 2 $游戏出现。这将动态系统的属性与组合图属性联系起来。我们通过表明普通的岩纸剪辑（RPS）在3循环上表现出混乱来对比，并且在带有$ \ geq 3 $ Vertices的一般图表上，带有RPS的网络复制器是汉密尔顿系统。这与既定的事实形成鲜明对比：RPS在标准复制器动力学或bimatrix复制器动力学中没有表现出混乱，该动力学与一个边缘和两个角度（$ k_2 $）的图形上的网络复制器相当。
We study the network replicator equation and characterize its fixed points on arbitrary graph structures for $2 \times 2$ symmetric games. We show a relationship between the asymptotic behavior of the network replicator and the existence of an independent vertex set in the graph and also show that complex behavior cannot emerge in $2 \times 2$ games. This links a property of the dynamical system with a combinatorial graph property. We contrast this by showing that ordinary rock-paper-scissors (RPS) exhibits chaos on the 3-cycle and that on general graphs with $\geq 3$ vertices the network replicator with RPS is a generalized Hamiltonian system. This stands in stark contrast to the established fact that RPS does not exhibit chaos in the standard replicator dynamics or the bimatrix replicator dynamics, which is equivalent to the network replicator on a graph with one edge and two vertices ($K_2$).
