The Emergence Of Cooperation And Its Dynamics Under The Involvement Of Antisocial Punishment In Spatial Prisoner’s Dilemma Model

Global issues such as the impact of COVID-19,the wide gap between the rich and the poor,natural disasters and energy crisis have been affecting people’s daily life and economic and social development.To overcome the problems of human existence and promote economic and social development are inseparable from the high degree of unity and cooperation between countries or individuals.However,the assumption of people engaged in economic activities in economic society in economics is abstracted as "rational-economic man",that is,everyone is self-interested and every behavioral decision tries to obtain the maximum economic benefits with the minimum economic cost.So how do cooperative systems evolve and how do cooperative systems maintain their stability? Evolutionary game theory is an effective tool for solving problems related to the emergence and maintenance of cooperation.Many studies have used it to explain the phenomenon of cooperation and even to look for rules that promote cooperation on a larger scale,such as kin selection,direct reciprocity,network reciprocity,punishment,loners and so on.Prisoner’s Dilemma Game is one of the theoretical model that presents social dilemmas in which individual and collective interests conflict.In the traditional two-strategy game,in which only cooperators and defectors participate in,both under the framework of evolutionary game theory and natural selection,the defector is dominant.If the loner is introduced into the two-strategy game,then the defector invades the cooperator,the cooperator invades the loner,and the cooperator invades the defector,which forms a rock-paper-scissors cycle.Further,on the basis of the three strategies,if the prosocial punishment is introduced,the punishment of the free rider will generally promote the evolution of cooperation.There is a study extending the optional public goods game to introduce full set of punishment strategies in finite population,in which punishment no longer promotes cooperation,a large number of antisocial punishment is favored by selection in a wide range of parameters,and loners are the main supporters of antisocial punishment.Besides,behavioral experiments are also conducted to verify aforementioned conclusions.There is another study combining prosocial punishment and antisocial punishment with network reciprocity.It is found that even if network reciprocity is weak and antisocial punishment exists,cooperation is dominant in a certain range of parameters.Network reciprocity explains the emergence of cooperation from the structure of interaction between individuals.In view of the fact that the evolution process of punishment mechanism on structured interactive networks is still lacking of systematic discussion,this paper combines the aforementioned full set of punishment strategies with network reciprocity to obtain the model studied,and explores the emergence of cooperation and its dynamics under the involvement of antisocial punishment in the optional Prisoner’s Dilemma Game.The research work is carried out in three steps.Firstly,the emergence of cooperation and its dynamics under the full set of punishment strategies in complex networks are explored from a broad perspective.We find that in complex networks,the full set of punishment promotes the successful co-evolution of cooperation and punishment,but inhibits the evolution of antisocial punishment.Secondly,this model is compared with the previous models.It is found that in complex networks,compared with the situation of no punishment,the full set of punishment promote cooperation.Though compared with the strategies with only prosocial punishment,the full set of punishment lead to a slight decrease in the level of cooperation,which is mainly caused by antisocial punishment,prosocial punishment and loners ensure a high level of cooperation in the full set of punishment strategies.Compared with Rand and Nowak’s model,the effect of network reciprocity leads to the effect of the full set of punishment on the evolution of cooperation and antisocial punishment is different from that without network reciprocity.Finally,we explore the influence of antisocial punishment on the evolution of cooperation and the dynamics of antisocial punishment in complex networks.It is concluded that in complex networks,the higher the antisocial punishment level is,the lower the level of cooperation is.Prosocial punishment has a greater effect on cooperation than antisocial punishment does.And antisocial punishment exists by forming rock-paper-scissors dynamics with other strategies,forming neutral drift with other strategies or complete dominant.For the innovation,in terms of mechanism design,this study explores the existence form of antisocial punishment including loners and its influence on the dynamics of cooperation’s emergence and maintenance in the interactive network for the first time by using multi-agent model,and explores the multi-strategy and multi-steady-state dynamic process in the full set of punishment strategies including loners for the first time.In terms of research methods,the results of this model are compared with those of related models.In addition,this study reflects the characteristics of interdisciplinary research.In a theoretical sense,this study further complements and improves the evolutionary game theory on the emergence and maintenance of cooperative behavior,and helps to deepen our understanding of network structure,reciprocity mechanism and the relationship between them.In a practical sense,this study is helpful to explain some realistic scenarios of antisocial punishment,and has a high reference value for management aspects such as reward and punishment mechanism design.It can also inspire us to strengthen the awareness of teamwork cooperative ability.Finally the process of obtaining the results helps to improve our skills and problem solving ability.