Research On The Cooperative Evolution Of Spatial Public Goods Game Based On Punishment Mechanism

Cooperation exists everywhere in life,and the cooperative behavior evolution research on the existence of biased individuals has become a hot,evolutionary game theory provides a convenient theoretical support for the study of this research topic.Evolutionary game theory is a kind of theory that combines classical evolution theory and dynamic evolution process to provide an effective methodological explanation for evolutionary cooperation in the group.In addition,group game is more common in real life,such as: the distribution of social welfare,the use of public resources,which are related to the group,then public goods game is introduced to study such phenomena.Public goods game is widely found in nature and society,it includes all the elements of society basically,and constitutes the indispensable cornerstone of our society and nature.According to the Darwinian theory,the individual will choose to betray to maximize his own payoff,which can not explain the cooperative behavior everywhere in the real world obviously.Based on this and punishment mechanism,some characteristics of people are added to the game individual,and the emergence and evolution of the cooperation between the game individuals are studies in the space evolutionary game.The main work is as follows:1.Based on mutual punishment mechanism,the cooperative evolution of the spatial public goods game with patience is studied.There exists a patience when we treat everyone or anything around us in real life,so we introduce patience in this paper,and the evolution of cooperation in the space public game is studied after the introduction of this parameter.The results show that when multiplication factor r is fixed,the greater expectation value is,the lower the system cooperation level is;and the higher multiplication factor r will promote the evolution of the cooperation when public expectation is constant.At the same time,the dynamic evolution pattern of the system is obtained by MATLAB software,and the dynamic evolution process and regularity of the system are illustrated by using the pattern.Marine issues,deforestation,public medical problems and so on are problems of public goods game,and when patience is introduced into the traditional public goods game model,which will make individual of the game to make judgments and decisions closer to human thinking,so it makes the solution of problems of public goods game in society closer to reality.2.The mechanism of conditional mutual punishment is put forward,and the influence of this mechanism on evolutionary cooperation is studies in the spatial public goods game.The mutual punishment is based on the gap of the two sides' strength in the real life,one side of the strength is strong enough to punish the other side.Inspired by this,the mechanism is proposed,not only the two individual' strategies are different,but also their payoff must reach a threshold,thus they can be punished each other.In order to understand the influence of mutual punishment mechanism on cooperative evolution in the spatial public goods game,the influence of mutual punishment threshold and multiplication factor on the final cooperation level of the system are studied,and it can be found that when the mutual punishment threshold and multiplication factor take the appropriate value,it can promote cooperative behavior effectively.This mechanism provides a reference for explaining the phenomenon of cooperation in the game of space public goods.When people encounter real social problems,the interaction of individuals is often conditional,so the research of this mechanism can provide reference for explaining and understanding the cooperative behavior of similar phenomena in society.3.The cooperative evolution of the spatial public goods game with patience is studied under conditional mutual punishment mechanism.Based on the previous research,the patience and conditional mutual punishment mechanism are combined to study the evolution of the system.The results show that the cooperation level of system decreases with the increase of public expectation when the multiplication factor is equal to each other.When the multiplication factor is constant,the system's cooperation level increases with multiplication factor gradually.If public expectation and multiplication factor are fixed,the cooperation level of system increases with conditional punishment threshold,but the stability value of system's cooperation level will decrease gradually with the increase of the public expectation,especially when the public expectation is 2,the conditional punishment threshold is 3,the change of multiplication factor has little effect on the stability value of the system's cooperation level.