Effects Of Memory,Field And Noise On Prisoners' Dilemma Game System

We study the effects of memory effects,noises,and external fields,on the evolution outcomes of a prisoner's dilemma game theory introduced in Ref.[1].Especially,the classical prisoner's dilemma game theory can explain why two gaming units are inclined to defect each other when their cooperation can obviously lead to better payoff.This model has also found extensive applications in politics and economics.In this thesis,we study the gaming processes on a square lattice,in which,for each step,each agent on a lattice site will game against its neighbors once.The gaming strategies will depend on the states of the neighbors and the agent's own payoff.By adjusting the external field and the payoff for betrayal,the final percentage of cooperators varies respectively.We discussed the effects of memory effects,noises,and external fields on the gaming of prisoner's dilemma.First we introduced memory effect into our interested system.Memory effects are commonly encountered in epidemic processes,and are widely found in different complex systems.In our model,the memory effect is introduced by assigning memory to some randomly chosen lattices,so that they can hold more information in making decisions.Secondly,noises are ubiquitous in all real systems,the effects of which should be treated with care.In this thesis,Gaussian white noise is imposed on the lattices to affect their behaviors.What is more,the gaming units will not necessarily follow' their "wiser" neighbors,the effect of this irrationality can be well described by introducing an external field.When this external field is absent,the lattices will unconditionally line up with their "wiser" neighbors.As this external field becomes stronger,the lattices will behave more and more randomly.The simulations indicate the following three conclusions:(1)Memory effect will increase the number of cooperators,and longer memory duration will enlarge the overall payoff.For our L=1000 system,when taking the strength of the external field to be K=0.1 the betrayal temptation coefficient b=1.5,and the remember duration to be 2,the percentage of cooperators is 37%higher than the system with the same settings other than the memory duration being 1(no memory effect);and the payoff expectation is also 32%higher.(2)Stronger external field will decrease the number of cooperators and the payoff expectation.For our system with L=1000,b=1.5,and K=0.15 when increase the strength of the external field to K=0.2,we observed a-3%decrease of cooperators,and a-6%decrease of payoff expectation.The larger K takes,the larger the decreasement.Furthermore,we also observe that for a hybrid system with at least two types of lattices,the external field doesn't affect they differently in a noticeable way,(3)Noises will disturb the cooperation processes,which works particularly well for homogeneous systems.However,for an inhomogeneous system,noises have no much impact on the payoff expectation of the system.For our homogeneous system,with L=1000,b=1.5,and the standard deviation for Gaussian noise 0.1,the number of cooperators will be 7%less,and the payoff expectation will be 8%less,comparing to the same system without noise(?=0).