Research On The Game Dynamics Of Complex Network Evolution Based On Public Goods Game

Evolutionary game theory provides an effective theoretical framework for the study of human behavior.It can not only describe the interaction between individuals,but also conduct theoretical abstract modeling.With the development of complex network theory,network evolutionary game theory has gradually become a complete and independent discipline,and then many researchers focus on the evolutionary game dynamics in networks.Through the theoretical simulation of individual behavior,Network evolutionary game can reveal the evolution mechanism of individual behavior in different network,which plays an important role in understanding decision-making behavior of individual in the realistic dilemma.The public goods game is a classic multiplayer game model for solving the tragedy of the Commons.Studying individual behavior and promoting the cooperative evolutionary mechanism of the population are of great significance for understanding group behavior in complex systems.Based on the public goods game model,in this paper we respectively study the evolutionary dynamics of cooperation in clustered scale-free networks and hyperbolic networks.The mainly contents of this article is as the following:Firstly,we study the evolution trajectory of cooperation strategies in clustered scale-free networks which based on a preference connection growth mechanism.Clustered scale-free network is one of the most classical scale-free network models,and it can truly describe the topological characteristics of real systems.Therefore,the study on the evolution of cooperation in clustered scale-free network is helpful to understand the emergence mechanism of cooperation in real network.Based on the repeated public goods game model and Fermi dynamics update rule,we investigate the evolution of cooperation on the network by numerical simulation.It is revealed that the frequency of cooperators ascend with the increase of the enhancement factor.Then we investigate the evolution of cooperation on clustered scale-free network with different average degree or clustering coefficient and find the influence of average degree and clustering coefficient on the evolution of cooperation is monotonous.But we also find the influence of the level of irrationality of individuals in public goods game model is non-monotonic.Finally,there are a conclusion that when the enhancement factor of individual is associated with the degree,cooperator can emerge on the network only if the correlation is positive.These findings may shed lights on better understanding the evolution mechanisms of cooperation in complex network,and have important theoretical value.Secondly,in this paper based on the repeated public goods game model and Fermi dynamics update rule,we investigate the evolution of cooperation strategies on hyperbolic network which based on popularity and similarity growth mechanisms.Although hyperbolic networks and clustered scale-free networks are generated based on different growth mechanisms,they are both scale-free networks which satisfying power-law distribution.Studying the evolution of cooperation in hyperbolic networks is helpful to understand the influence of network structure on the evolution of cooperation,and also helps to explore the mechanism of cooperation evolution in real scenarios.The numerical simulation method is used to study the evolution of the cooperation strategy on the hyperbolic network.Compared with the evolution process in the clustered scale-free network,it is found that cooperation has different evolution mechanisms in these two types of networks.It can be found that there exist the so-called metric clusters of cooperators on the hyperbolic network and cooperator can diffuse through those metric clusters.However,cooperation strategies firstly diffuse among hubs and form connected clusters.Then cooperation can diffusion through those connected clusters on clustered scale-free network.We also investigate the effect of the average degree,clustered coefficient and the noise parameter on evolution of cooperation.There are similar result on hyperbolic networks and clustered scale-free networks.Therefore,these studies may inspire new thinking about understanding the emergence of cooperation on complex networks.Finally,we investigate the evolutionary dynamics of cooperation,half-cooperation and defection strategies on regular graphs and scale-free networks.Through micro analysis of the spot graph,we can find cooperators and half-cooperators will form the cluster to resist invading defectors and in the end only cooperator can be found on regular graph.However,through analysis degree distribution of strategies,half-cooperators coexist with cooperators by forming clusters on scale-free network.These conclusions provide an important reference for us to study individual decision behavior and cooperative.