The Study Of Evolutionary Game Theory Based On The Perspective Of Three Strategies

As the third principle of evolution based on mutation and natural selection,cooperative behavior exists both in nature and society universally.However,it has always been a puzzling question that how such an altruistic behavior generated and persisted in contemporary world with fierce competition.Based on this,many scholars in various fields have also done a lot of related research.Among them,Martin Nowak attributed the arise of cooperation to five mechanisms: direct reciprocity,indirect reciprocity,network reciprocity,group selection and kin selection.We will explore the evolution of cooperative behavior from the perspective of network reciprocity and direct reciprocity respectively in the context of three strategies.Here,we introduced the third strategy into traditional prisoner's dilemma game,which can only cooperate or defect.Based on the framework of evolutionary game theory,we explored how historical payoff mechanism and teaching activity mechanism affect the evolution of cooperation in voluntary prisoner's dilemma game with structured population.Here,voluntary prisoner's dilemma game signifies introducing voluntary participation strategy,which is called "loner".And it is worth to mention that "loner" and his opponent will always acquire a small but fixed payoff.As for the model,historical payoff mechanism means that the calculation of fitness considers the current payoff and last step payoff simultaneously,while teaching activity mechanism refers to control the probability of strategy updating by introducing a parameter.The numerical results through simulation demonstrated that both two mechanisms can facilitate the evolution of cooperative behavior in the context of three strategies.Then,we explored the evolution of cooperation in the context of the three strategies by designing experiment in this paper.We introduced super-defection strategy,which is a kind of defective behavior with higher intension,and investigated the variation of average frequency of cooperation under different payoffs of super-defection strategy.The participates of this experiment are undergraduates from Yunnan University of Finance and Economics.In this paper,we analyze this numerical result from the perspective of the average frequencies of strategies,correlation between average frequencies of strategies and average payoffs,strategies response,time evolution of strategies,distribution of average frequencies of strategies and dilemma strength,respectively.In addition,we also did statistical test to verify the accuracy of results.And we constructed generalized linear mixed model to analyze further.The results showed that the introduction of super-defection strategy can not promote the evolution of cooperative behavior.Especially,the evolution of cooperation could be effectively restrained when payoff of super-defection strategy is high.The analysis result of model also validated the same consequence.Beyond that,it indicated that older individuals prefer to choose super-defection rather than cooperation,and men are more willing to cooperate than women,while women are more likely to choose defection and super-defection strategies.The work in this paper will help people to understand the emergence and evolution process of cooperative behavior.It will make a heuristic influence on relevant subjects such as bioecology,anthropology,psychology and sociology.In addition,the study of this issue will help to solve a series of environmental problems such as pollution and exhaustion of resources.And it will also have some practical significance for exploring the spread and prevention of epidemics.