Evolutionary Game On Complex Networks

In the past ten years,complex network and the dynamics on it becomepopular topics of statistic physics and nonlinear physics.Evolutionarygames,an important dynamics in complex networks,have also show morecomplicated behaviors.At the beginning of this thesis,we review some network structureparameters like degree distribution,clustering coefficient,and some typicalnetwork structures like regular network,random network,small-worldnetwork,and scale-free network.Then we present some game models andexplain the concept of Nash equilibrium.In the second section,we introduce how to study the evolutionarygame on graph.We depart this topic to four independent modules and introducethem separately.These introductions are help for readers to readother papers.The traditional physical system can be reproduced qualitativelywell by mean-field approximation.This appropriate description of anevolutionary game requires more sophisticated technique.We introduce ageneral mean-field approximation that can analyze the evolutionary gameson regular network.Then we study the synchronization between the prisoner's dilemmagames with voluntary participation in two Newman-Watts small-world networks.It is found that there are three kinds of synchronizations:partialphase synchronization,total phase synchronization,and complete synchronization,for varied coupling factors.Besides,two games can reach completesynchronization for the large enough coupling factor.We also discussthe effect of the coupling factor on the amplitude of oscillation of cooperatordensity. In the forth section,we study the effect of memory on the evolutionofthe prisoner's dilemma game in square lattice networks.Based on extensivesimulations,it shows that the density of cooperators is enhancedby an increasing memory effect for most parameters.However,we also observethat the density of cooperators decrease with an increased memoryeffect in the case of a large memory and moderate temptation.It is interestingto note that memory makes cooperators immune from temptation.The strength of protection reaches its maximal value only for a moderatememory effect.In the fifth section,we build a coevolution model of prisoner's dilemmagame and network structure to study the dynamic interaction in the realworld.Different from other game and network structure coevolution models,players rewire their network connection according to other players'payoffs.We use a parameterαto control the effect of payoff in the processof rewiring.Based on the asynchronous update rule and Monte Carlosimulation,it is found that,when players prefer to rewire their links to thericher,the cooperation density will increase.The reason of it is analyzed.At last,we make a conclusion and outlook of this thesis.