Research On The Cooperative Evolution Dynamics Under Income Redistribution Policy

"Natural selection,survival of the fittest" is the core of Darwin’s theory of evolution,emphasizing that both biological individuals and human beings are selfish,and individuals tend to choose to betray(hitchhiking)to obtain higher benefits,which is consistent with the hypothesis of "rational man" in the classical economic theory,that is,every person engaged in economic activities takes economic actions to try to obtain greater economic benefits at their own minimum economic cost.However,from microbial communities,social animals to human society,cooperation is a common phenomenon in nature.Exploring how cooperation is generated and maintained has become an important challenge including economics,biology,sociology and other disciplines.Among them,income redistribution,as an important means of adjusting economic relations and income distribution,refers to the process of income adjustment among social members by means of taxation and transfer payment,based on the results of the initial income distribution.Income redistribution is of great significance in adjusting the income gap of residents and promoting the fairness of income distribution.It is also an important part of achieving common prosperity.Then,how will the income redistribution process affect the cooperative behavior choice of individuals and groups through the adjustment of income? Pei et al.considered a simple income redistribution model in the dilemma of traditional public goods,that is,individuals need to pay tax on the initial income according to a given "tax rate",and the income in the tax pool is evenly distributed among all individuals.The research results show that the increase of "tax rate" has greatly promoted the prosperity of cooperation and the improvement of welfare.However,the income redistribution mechanism in reality is more complex than the above model.This paper uses the public goods dilemma model,based on evolutionary game theory,to design a more realistic income redistribution mechanism,and carries out computer simulation through Monte Carlo method to further study the impact of income redistribution policy on cooperative behavior and welfare evolution.The main work of this paper is as follows: individuals gain initial income from the game of public goods,and the innovation of income redistribution mechanism is mainly reflected in the introduction of threshold A to measure whether individuals meet the conditions for participating in the redistribution process.The first income redistribution model is: referring to the individual income tax in the tax system,tax will be paid only when the individual income reaches the given standard,that is,if the initial income of a group member reaches or exceeds the threshold A,the individual needs to transfer the p proportion of its initial income to the redistribution pool,and then the total income in the redistribution pool is evenly distributed to all members of the group;The second income redistribution model is: first,all members of the group are subject to compulsory taxation,that is,all members of the group need to transfer the p proportion of their initial income to the redistribution pool,and then the accumulated tax in the redistribution pool is evenly distributed to the members whose residual income is lower than the threshold A,which is equivalent to subsidies for low-income people.Among them,the mandatory taxation of group members mainly refers to the poll tax system.The research in this paper mainly focuses on the influence of redistribution ratio p and threshold A on the evolution of cooperative behavior and its dynamic process,and explores the causes of relevant phase transitions from the macro and micro levels,respectively,and finally discusses the impact of different gain factors on the level of cooperation.In addition,this paper further discusses the case of threshold A as a co-evolutionary parameter.The main conclusions of this paper are as follows: First,compared with the previous income redistribution model,when threshold A is introduced,even if the redistribution ratio p is very small,the level of cooperation can occur,and the cooperation rate increases with the increase of the redistribution ratio p.Accordingly,the increase in cooperation rate also led to a significant increase in the average income(welfare)of the group.This shows that redistribution according to the different income levels of members can more accurately transfer part of the income of highincome people to low-income people,effectively weakening the advantages of defectors,and promoting the prosperity of cooperation and the improvement of welfare.Secondly,it is found that the change of cooperation level presents a firstorder phase transition phenomenon,that is,the cooperation level will suddenly rise or fall with the change of threshold A,where the first-order phase transition point is closely related to the income of team members,especially the cooperative individuals.More accurately,the threshold A corresponding to the phase transition point is exactly the income of the partners in all possible strategy components.Finally,it is found that there are some specific ranges in threshold A that make the cooperation level higher,that is,an appropriate redistribution threshold that gives priority to the benefits of partners can better promote the cooperation level.In addition,the stability of the above conclusion is further confirmed by the change of gain factor.