Exploring Evolutionary Dynamics On Complex Networks

In this thesis,we explore the promotion and inhibition of cooperation induced by diversity of rationality in the evolutionary games on complex networks.Our main works are showed as following:1.Diversity of rationality affects the evolution of cooperation on heterogeneous networks: By modifying the Fermi updating rule,we introduce the diversity of individual rationality to the evolutionary game dymanics under heterogeneous network topology,and our results shows that this diversity heavily influences the evolution of cooperation.Cluster-forming mechanism of cooperators can either be highly enhanced or severely deteriorated by different distributions of rationality.Slight change of the rationality distribution may transfer the whole system from the global absorbing state of cooperators to that of defectors(in our work the severe deterioration is called cooperation crisis).Based on mean-field argument,quantitative analysis of the stability of cooperative clusters reveals the critical role played by agents with moderate degree values in the evolution of the whole system.The inspiration from our work may provide us a deeper comprehension towards some social phenomena.2.Diversity of rationality affects the evolution of cooperation on homogeneous regular networks: After introducing the distribution of rationality generated from a BA scale-free network to the regular lattice,we have gained considerably different,even opposite,findings,compared with the results obtained on scale-free networks.In the parameter region where cooperation is highly promoted on scale-free networks,it is severely inhibited on regular lattice;in the parameter region where cooperation crisis takes place on scale-free networks,the frequency of coopertors may have a sudden peak,which we call cooperation explosion in our works.On regular lattice,the heterogeneity of the rationality distribution can not maintain the robustness of cooperation except in narrow parameter range,where cooperation explosion occurs.3.Diversity of rationality affects the evolution of cooperation on small-world networks: After introducing the distribution of rationality generated from a BA scale-free network to the spatial distance-dependent small-world networks(SDSW network),we gain four findings: (1) A critical value of parameterβ:β_C exists in the region where cooperation crisis takes place on the scale-free network,and the corresponding rationality distributions in the case ofβ＞β_C can highly promote cooperation,as well as its robustness towards the variation of the average rationality value.(2) Diversity of rationality is able to intensify the deviation from the widely applicable rule:the fewer connections there are,the easier it is for natural selection to promote cooperation;(3) Diversity of rationality determines the influence of the cluster coefficient on the evolution of cooperation:they respectively have non-monotonous and monotonous relationship on the two sides ofβ_C;(4) if the agents with largest(or smallest) rationality values are interconnected, the phenomenon similar to the cooperation crisis on scale-free networks appears around the region ofβ=0.