Evolutionary Dynamics Of Cooperation On Interdependent Networks

Evolutionary dynamics on complex networks is one of the most popular topicsbehind many scientific disciplines. The combination of evolutionary game theory andcomplex networks provides a convenient and systematical framework to study theevolution of cooperation between unrelated individuals. In this thesis, we firstly make abrief introduction of the evolutionary game theory and complex networks. Then, wedevelop two simple but effective models of the evolutionary dynamics of cooperationbased on interdependent networks to investigate the evolutionary dynamics on them.The main results and innovative points of this thesis are as follows:First, a model of interdependent networks including two interacting networks withthe same structure and size is constructed. We introduce public goods game into such asystem to study the impact of probabilistic interconnection on the evolution ofcooperation of the whole system and the coupling effect between two layers. Simulationresults show that there exists an intermediate interconnection probability leading to themaximum cooperation level in the whole system. Also, the fraction of internal linksbetween cooperators of two layers is maximal correspondingly at the optimalinterconnection probability. Moreover, even if initially there are no cooperators in onelayer of interdependent networks, cooperation can still be promoted by probabilisticinterconnection, and the cooperation levels in both layers can more easily reach anagreement at the intermediate interconnection probability.Second, the prisoner’s dilemma game and snowdrift game models are introducedcorrespondingly to two layers of a new model of interdependent networks to investigatethe evolutionary dynamics on them and the interaction effect between them. Numericalsimulation results show that two layers of interdependent networks can strongly effecteach other by the influence probability between them, where the effect intensityincreases with the increasing probability. For the layer with lower cooperation level,there exists an optimal influence probability promoting the evolution of cooperationfastest. Moreover, it is worth noting that the introduction of influence probability canfundamentally effects the formation of clusters on the layer playing prisoner’s dilemmagame, which further influences the micro-dynamics of evolution of cooperation on it.