The Evolution Of Cooperation In Spatial Public Goods Game With Conditional Punishment Strategy

Cooperation plays an extremely important role in human development.Rational individuals driven by the temptation of interest will not sacrifice their interests to cooperate.When the pursuit of maximizing personal interests conflicts with collective interests,it can lead to a situation unfavorable to all,which is known as a “social dilemma”.Numerous experts and scholars in diverse fields have been concerned about the puzzle of cooperation.Evolutionary game theory provides a theoretical framework for studying this type of issue.In particular,the public goods game(PGG)is one of the paradigms to explore cooperative behaviors in multi-player interactions.In this context,several mechanisms have been proposed to promote the evolution of cooperative behaviors,among which the punishment mechanism is favored.In human society,compliance with the law is maintained through sanctions.If the law is broken,a penalty will follow.Therefore,timely punishment allows us to avoid engaging in illegal activities.In reality,individuals tend to punish other participants based on specific conditions,rather than punish them directly.Thus,this paper takes the perspective of conditional punishment and introduce three different conditional punishment into traditional spatial public goods game.Some methods of mathematical modeling and computer numerical simulation are used to explore how the level of social cooperation evolves under three different mechanisms.The main work of this paper is as follows:We consider a reputation-based exclusion strategy in the public goods game.Players with this strategy expel defectors based on the reputations of the defectors.We analyze the level of cooperation and the dynamic process of the evolution of the strategies.It can be found that the conditional punishment mechanism facilitates the emergence of cooperation.Meanwhile,we have also extended the condition that the punishers rely on when imposing punishment,considering the tolerance to the reputation of the opponent.It is found that the increase of threshold is good for the evolution of cooperation.Exclusion promotes the evolution of cooperation by excluding free-riders.How will the level of cooperation and the frequency of strategy evolve in the population when exclusion is combined with punishment? In reality,the sanctions for offenders vary with different circumstances,and the regulatory agencies consider factors such as the reputation of the company when penalizing the company.Based on these,we further introduce conditional punishing that allows punishers to switch between traditional punishment and exclusion based on reputation.Sanctioners adopt different forms of punishment based on the reputation labels of defectors.The results show that a smaller reputation threshold can significantly promote cooperation,and when the punishment fine increases,the range of synergy factor in which cooperation and defection can coexist in the system is smaller and phase transition occurs more easily.On the other hand,the increase in exclusion costs can harm the evolution of cooperation,and the defectors are more and more rampant.Different from the above research,we change the conditions under which the punisher applies different sanctions,that is,imposing punishment or exclusion is based on the number of defectors in the group.Compared with the traditional model,conditional punishment can effectively promote cooperation,and the increase of the threshold can enhance the level of cooperation.Combined with the reality,the smaller the threshold,the worse the implementation of the exclusion,which results in a smaller probability of successful exclusion.When the exclusion probability raises,we can find that the value of the synergy factor for the emergence of cooperation declines as the threshold increases.This thesis introduces three conditional punishment strategies in the spatial public goods game to study the influence of conditional punishment on the evolution of cooperation.By summarizing the simulation results of these models,the research on the conditional punishment mechanism for promoting cooperation is further supplemented,which makes the punishment mechanism closer to reality.At the same time,the research of conditional punishment in this paper also has important practical significance,such as providing important ideas for formulating reasonable conditional punishment strategies.