Research On Cooperative Behavior Based On Heterogeneity Of Updating Rules In Structured Population

With the rapid development of the times,people now live in a world full of all kinds of complex networks.For example,social network,transportation network,communication network,power network,financial network and so on,these networks not only improve our quality of life,but also bring some negative impacts.Among them,evolutionary game theory provides a powerful theoretical framework for solving the generation and maintenance of cooperative behaviors among selfish individuals in complex networks.Through this framework,this paper uses effective scientific methods to explore and explain the reasons for alleviating various dilemmas in social life.In recent years,most researches have explored the evolution of cooperation in structured groups by introducing various effective mechanisms.However,when we discuss the dynamics of evolutionary game,the role of strategy update rules should not be ignored.Therefore,this paper proposes two new evolutionary game models,focusing on the role played by the heterogeneity of strategy update rules in cooperative evolution.The main research contents and innovations of this paper are as follows:1.In the mixed strategy game model with uncertainty of memory mechanism and individual decision-making,the effect of heterogeneity of strategy update rules on the evolution of cooperation is mainly discussed.In this paper,Moran-like process is proposed,which realizes the preference selection of the focal individual to the neighbors in the game,and is compared with Fermi rule and the random neighbor selection method used in Replicator dynamics(RD).Through a large number of simulations,it is found that Moran-like process can promote the emergence and expansion of cooperation clusters faster and achieve a higher cooperation frequency in most cases than the other two strategy update rules.It is proved that the strategy update rules play an important role in the evolution of cooperation in complex networks.In addition,this paper also discusses the influence of memory mechanism and mixed strategy on the evolution of cooperation.The results show that a longer memory length and a lower strategy adjustment factor are most beneficial to the evolution of cooperation.This shows that learning from individuals with firm strategies can effectively improve the degree of cooperation among groups.Finally,the model is extended to a wider range of structured networks,and its robustness is verified.2.Put forward an evolution model of heterogeneous willingness induced by different states of individuals,and introduce two different strategy renewal schemes and discuss their differences in cooperative evolution.Among them,as for the central individual to choose the teaching object,Scheme I tends to choose low-payoff neighbors,while Scheme II adopts random selection.In addition,the individual’s willingness to learn is influenced by the individual’s state,and the individual’s state will remain unchanged after the system is initialized.Through a large number of simulations,the two strategy updating schemes show great differences in promoting cooperative evolution.In Scheme II,because the focal individual can capture the neighbors with lower payoff to teach them,the system can achieve higher cooperation frequency in steady state.This shows that the strategy update rules play an important role in the evolution of cooperation.At the same time,it is also found that there are optimal busy individual ratio and willingness adjustment factor in promoting cooperative evolution.Finally,the model is simulated in a wider structured network,and its robustness is verified.