Evolution Of Cooperative Behavior In Mixed Update Rules

In the process of survival and reproduction in nature,cooperative behavior is very common.As an important part of the development of human civilization,scientists in many fields have made unremitting efforts to promote the development of cooperative behavior.Based on the Prisoner’s Dilemma framework,this paper first uses a dynamic system model to analyze the conditions under which the infinite population under the aspiration update rule and the conformity update rule will promote cooperation,and analyzes the stability of the equilibrium point,and then explores the evolution of cooperative behavior under the mixed update rules in the network population.First,in the Prisoner’s Dilemma,this paper combines a dynamic system model to analyze the impact of parameters such as the ratio of cost to income,the average expectation level of cooperative players and the average expectation level of betrayed players on the cooperative evolution of infinite population in the aspiration update rule and the conformity update rule,and the stability of the equilibrium point.Through the research,it is found that when the ratio of the cost that the collaborator needs to pay to the income that the collaborator gains is small,it is beneficial to cooperation.The average expectation level of cooperative players decreases,while the average expectation level of betrayed players increases,which is conducive to the realization of cooperation.With regard to the stability of fixed points,it can be found that the average expectation level of cooperative players has an important impact on the stability of evolution.The aspiration update rules will be more stable than the conformity update rule,and the area where the initial partner proportion is small and the fixed point tends to be stable is larger.Secondly,this paper conducts a prisoner’s dilemma game in a square grid network with periodic boundaries,and observes the evolution process of cooperative behavior based on three update rules(imitation update,self-reflection update or conformity update).This paper proposes a new idea,adding the concept of experience accumulation in the process of re-evolution,that is,it is possible to change the strategy update rule after the participants have played multiple rounds of games.Through analysis,it is found that the accumulation of experience and the temptation of defection have a significant impact on the participants’ choice of action(cooperation or defection)and update rules.The conformity update rule only exists when the value of experience accumulation is very small,and the self-reflection update rule also wins for a short time as the accumulation of experience increases slowly.When the accumulation of experience reaches a certain amount,the influence of the temptation of defection on the evolution process becomes stable,with the increase of the temptation of defection,defectors based on the imitation update rule eventually occupy the dominant position.When the temptation of defection is slightly higher than the benefit of cooperation,it is conducive to the development of cooperation.The research on the evolution of cooperative behavior and the stability of fixed points in this paper is conducive to the emergence and development of cooperative behavior.