Effect Of Migration On The Cooperation Of Evolution Game Theory

As M.A.Nowak described in the book "evolutionary dynamics: the equation of life",cooperation is the third major evolutionary dynamics,in addition to natural selection and genetic mutations.But different from the latter,cooperation didn't exist at the emergence of life,but a natural selection results with the biological diversity and the formation of the organization.The widespread existence of cooperation in nature is contrary to the traditional view of biological individuals are limited by the time,space and their own ability and often tend to make the protection of their own interests.Therefore,why cooperation can be produced and developed in the population composed of selfish individuals has become an issue to biology,sociology and many other areas of scholars.Evolutionary game theory is an important theoretical tool to study the evolution of cooperation by using game theory and mathematical model.Based on this theory,the mechanism of kin selection,direct reciprocity,indirect reciprocity,group selection,network reciprocity and so on,which can simulate the emergence of cooperative behavior and explain the mechanism of cooperation,are proposed.In recent years,network reciprocity has confirmed that some structured populations can affect the evolution of cooperation,such as lattice networks,scale-free networks and small-world networks.Further studies have found that the migration mechanism of simulating natural biological migration can accelerate the formation of cooperation and improve the cooperation level of population under certain conditions.For example,in the evolution model based on lattice network,three kinds of migration strategies are proposed: random,success-driven and self-adaptive migration.However,these migration strategies have imperfections,such as random migration strategy of unconditional movement makes population structure degenerated into approximate unstructured,adaptive migration is only applicable to scene that individual information is limited to access,benefit transfer only consider their own income and makes the cooperators surrounded by defectors in the migration dynamic,resulting in the population cannot achieve pure cooperation even under a very favorable condition for cooperators.In addition,all of the existing research apply the update rules of the standard lattice game in the model with migration mechanism,which cannot effectively describe the spatial characteristics of the migration mechanism.And there are also differences in the models used in the research of different migration strategies.It leads to the lacking of a unified model for horizontal comparison between strategies.To solve these problems,firstly,this paper proposes a new update mechanism,this mechanism makes the imitator move to a position adjacent the producer,to simulate real-world learning strategies or reproductive behavior.Then,based on the classic lattice network prisoner's dilemma game model,present three new migration strategy: failure-driven migration,hate-driven migration and global migration,and compared the results and effects of different migration mechanism under population density change,strategy mutation scenarios and different evolutionary process.The experimental results show that those strategies not only solve the existing problems but also promote the cooperation level and accelerate the evolution process,the failure-driven strategy perform better than other migration mechanisms in most cases of cooperative evolution.Finally,aiming at the shortcoming of success-driven migration that cooperative clusters surrounded by the defectors,we present a new migration strategy that consider both self-benefit and fairness factors.Through the simulation experiment analysis of the cooperator proportion changes and population snapshots,we find this strategy help individuals to find a block with higher fraction of the similar,so that under certain conditions the evolution of cooperation can reach the ideal state of pure cooperation,and this strategy can adapt to changes in population density,initialization parameter,mutation rate and strategy payoff matrix etc...This prove that the strategy not only compensate the shortcoming of success-driven migration,but also promote the evolution of cooperation.