Stability Analysis Of Asymmetric Prisoner's Dilemma Games

As a classical game theory model,the stability of the equilibrium point of prisoner's dilemma has been widely studied.As the asymmetry has a certain impact on the game cooperation,the stability of the equilibrium point of asymmetric prisoner's dilemma is discussed.Combined with the population games,evolutionary dynamics,evolutionary graph theory and other related theoretical knowledge,this paper studies the stability of the equilibrium point of asymmetric prisoner's dilemma game.Three kinds of asymmetric prisoner's dilemma game models are established:asymmetric repeated prisoner's dilemma game model with punishment mechanism,asymmetric prisoner's dilemma game model under spatial structure,asymmetric prisoner's dilemma game model with role.This paper discusses the conditions of cooperation in the above three kinds of asymmetric prisoner's dilemma games.It is found that in the asymmetric repeated prisoner's dilemma game model with punishment mechanism,punishment and discount factor can promote cooperation when they meet certain numerical constraints with asymmetric degree.Then,MATLAB software is used to simulate the results with several groups of parameters,and the conclusion is verified to be correct.In the asymmetric prisoner's dilemma game model with spatial structure,this paper studies the replication dynamics of asymmetric prisoner's dilemma model on the regular graph with degree k when it follows three different updating rules: birth and death process(BD),death and birth process(DB)and imitation process(IM).By comparing with the dynamic replication of the prisoner's dilemma model in the uniform field,it is found that BD update rules in the spatial structure do not significantly promote cooperation,while DB and IM update rules can promote cooperation when they satisfy a small degree k.For the role asymmetric prisoner's dilemma game,the evolutionary dynamics related knowledge is used to establish the role asymmetric prisoner's dilemma game model.In this paper,we discuss the stability of the equilibrium point,and finally get a conclusion similar to the standard prisoner's dilemma.No matter in player position 1or player position 2,betrayal is always the best choice for the agents in the two populations.