Evolutionary Game Model Of Prisoner’s Dilemma Under The Condition Of Direct Reciprocity And Group Selection

Cooperation exists widely in ecosystem and human life.Darwin’s theory can explain altruistic behavior,but it can’t explain the typical prisoner’s dilemma that widely exists in reality.To solve this problem,Nowak proposed five well known cooperative mechanisms on the basis of previous work,among the five mechanisms,direct reciprocity and group selection are the two most widely used ones.Based on the theory of evolutionary game theory,I create the evolutionary game prisoner’s dilemma model under two cooperative mechanisms,using direct reciprocity and group selection as decision variables.I also work out the strategy of evolution and replicator dynamics and correlation relationship analysis,which propose a new idea to explain what the “dilemma” is in the prisoner’s dilemma.The main contents of this paper are as follows:(1)I set up a prisoner’s dilemma evolutionary game model with direct reciprocity and group selection as the decision variables.The evolutionary stabilization strategy of the model was obtained.Using the theory of replicon dynamics and stability,the effect of the probability that the two sides of the game meet again in the next game on the stability of evolution and the evolutionary path under the condition of direct reciprocity is analyzed.At the same time,the influence of the number of entire groups and the number of individuals within the group on the evolutionary stability and evolutionary path under group selection conditions is also analyzed.The solution to the prisoner’s dilemma for direct reciprocity and group selection cooperation mechanisms has provided the possibility of moving from non-cooperation to cooperation.(2)This paper establishes a prisoner’s dilemma evolutionary game model under the condition of direct reciprocity and group selection.The equilibrium and evolutionary stability strategies of the model are calculated,and the probability of the two sides of the game encountering again and the influence of the number of entire groups and the number of individuals within the group on the evolutionary stability strategy and evolution path are analyzed.The results of the mechanisms were compared and the advantages of the two cooperative mechanisms working together were derived.