Research On Evolutionary Game On Complex Networks

In recent years,the studies of cooperative behavior about complex networks have been the hotspot in Physics,Mathematics and Economics,and obtained a very successful application in many ways.From individuals to countries,they have cooperative behavior to some extent.What kinds of network structure and the strategies can enhance the mutual cooperation ability between individuals has been the concern by many people. This paper studies that the age-correlation between individuals existing in growing random network of contacts (GR NOCs) with different degree distribution results in cooperation dominating over the entire range of their respective parameters for both prisoner's dilemma (PD) and snowdrift game (SG) .Firstly, we studied the cooperation behavior between individuals in tree GR NOCs of contacts with the average degree z = 2 and in ring GR NOCs with the average degree z = 4 on PD.We found that with the evolution of time t,the frequency of cooperators f_c on NOCs is oscillating. After some time,the oscillation will disappear and steady.The frequency of cooperators f_c is tuned by exponentγof the connection kernel Ak = kγ.The cooperative behavior is the most competitive on GR NOCs with the average connectivity z =2 atγ=1.25,which is a tree network,i.e.,the age-correlation in SF (γ=1.0) tree (z=2) NOCs is not strong enough to make the individual with high connectivity interconnected in optimal way.When the correlation between frequency of cooperators f_c and time t is weak, i.e.,the cooperation frequency f_c achieve the stable value in short time,the cooperation relies exclusively on the relative quantity b of the payoffs.Along with the increase of betrayal value b, cooperation frequency f_c reduced.when the correlation between frequency of cooperators f_c and time t is intense, i.e.,the cooperation frequency f_c achieve the stable value in short time, we found cooperation frequency f_c and betrayal temptation parameter b are irrelevant.Network structure will determine the cooperative behavior of the whole system.We also simulated that the cooperation behavior between individuals in ring GR NOCs with average degree z = 4.We found that the most competitive cooperative behavior is obtained atγ=1.0,i.e.,the age-correlation in SF (γ=1.0) ring (z=4)NOCs is strong enough to make the individual with high connectivity interconnected in optimal way. Meanwhile we also studied different distribution of strategy in initial networks does not affect final cooperative behavior of the whole network.Secondly,we studied the cooperation behavior between individuals in tree GR NOCs of contacts with the average degree z = 2 and in ring GR NOCs with the average degree z = 8 on SG.We also found a similar situation,the cooperative behavior is the most competitive on GR NOCs with the average connectivity z =2 nearly atγ=1.2,which is a tree network,and the cooperative behavior is the most competitive on GR NOCs with the average connectivity z =8 atγ=1.0,which is a ring network.Ours results are proved in practice with a lot of application value.