Study On The Evolution Game Model Of Indirect Reciprocal Prisoner's Dilemma In Different Forms

Cooperation is the most common phenomenon in nature,from single-celled microbes to advanced mammals,from social insects to human society.The cooperation among of organism greatly increases the living opportunity.But according to Darwinian evolution,natural selection is based on competition,and rational individuals are pursuing their own interests,which obviously cannot explain the pervasive cooperative behavior.Among all the cooperative mechanisms in nature,indirect reciprocity is a very important cooperative mechanism,but how to promote cooperation through indirect reciprocity is a difficult problem.As an effective tool of studying the complex interactive cooperative behavior of individuals in biological population and human society,evolutionary game theory provides a new idea for solving the mechanism of indirect reciprocal cooperation.In this paper,indirect reciprocity is implanted into the prisoner's dilemma model.Based on the evolutionary game theory,this paper discusses the two game forms of single round and multiple rounds,and finds out the corresponding evolutionary stabilization strategy and replicon dynamics,at the same time analyzes the influencing factors.This paper provides beneficial enlightenment for solving the "dilemma" phenomenon in prisoners' dilemma.Contributions of this paper mainly include:(1)Taking discrimination as variable,the evolutionary game model of indirect reciprocal prisoners' dilemma under single round conditions is established,based on the relevant knowledge of evolutionary game theory.At the same time,the equilibrium solution of the game model is obtained,and its evolutionary stability and replicon dynamics are analyzed.The influence of discrimination on cooperative behavior is discussed,and an evolutionary phase diagram is given,which provides a new explanation for the prisoner's dilemma from non-cooperative to cooperative.(2)Based on the knowledge of repeated game theory,this paper generalizes the model of indirect reciprocal prisoners' Dilemma under the condition of single round reciprocity,establishes the evolutionary game model under the condition of multiple rounds of reciprocity,and obtains the corresponding equilibrium solution.The evolutionary stability strategy and replicon dynamics are analyzed from the perspective of evolutionary game theory and the influence of discrimination on equilibrium results is discussed.Numerical simulation iscarried out,and the conditions for prisoners' dilemma to get rid of "dilemma" under the condition of multi-round game are given.