In this paper,we study the influence of the size of interaction neighbors(k) on the evolution of cooperation in the spatial snowdrift game.At first,we consider the effects of noise K and cost-to-benefit ratio r,the si...In this paper,we study the influence of the size of interaction neighbors(k) on the evolution of cooperation in the spatial snowdrift game.At first,we consider the effects of noise K and cost-to-benefit ratio r,the simulation results indicate that the evolution of cooperation depends on the combined action of noise and cost-to-benefit ratio.For a lower r,the cooperators are multitudinous and the cooperation frequency ultimately increases to 1 as the increase of noise.However,for a higher r,the defectors account for the majority of the game and dominate the game if the noise is large enough.Then we mainly investigate how k influences the evolution of cooperation by varying the noise in detail.We find that the frequency of cooperators is closely related to the size of neighborhood and cost-to-benefit ratio r.In the case of lower r,the augmentation of k plays no positive role in promoting the cooperation as compared with that of k = 4,while for higher r the cooperation is improved for a growing size of neighborhood.At last,based on the above discussions,we explore the cluster-forming mechanism among the cooperators.The current results are beneficial to further understand the evolution of cooperation in many natural,social and biological systems.展开更多
We combine the Fermi and Moran update rules in the spatial prisoner＇s dilemma and snowdrift games to investigate the behavior of collective cooperation among agents on the regular lattice. Large-scale simulations ind...We combine the Fermi and Moran update rules in the spatial prisoner＇s dilemma and snowdrift games to investigate the behavior of collective cooperation among agents on the regular lattice. Large-scale simulations indicate that, compared to the model with only one update rule, the the role of update dynamics should be paid more attention in cooperation behavior exhibits the richer phenomena, and the evolutionary game theory. Meanwhile, we also observe that the introduction of Moran rule, which needs to consider all neighbor＇s information, can markedly promote the aggregate cooperation level, that is, randomly selecting the neighbor proportional to its payoff to imitate will facilitate the cooperation among agents. Current results will contribute to further understand the cooperation dynamics and evolutionary behaviors within many biological, economic and social systems.展开更多
基金Supported by the National Natural Science Foundation of China under Grant Nos. 60904063 and 60673046Tianjin municipal Natural Science Foundation under Grant No. 11JCYBJC06600the Development Fund of Science and Technology for the Higher Education in Tianjin under Grant No. 20090813
文摘In this paper,we study the influence of the size of interaction neighbors(k) on the evolution of cooperation in the spatial snowdrift game.At first,we consider the effects of noise K and cost-to-benefit ratio r,the simulation results indicate that the evolution of cooperation depends on the combined action of noise and cost-to-benefit ratio.For a lower r,the cooperators are multitudinous and the cooperation frequency ultimately increases to 1 as the increase of noise.However,for a higher r,the defectors account for the majority of the game and dominate the game if the noise is large enough.Then we mainly investigate how k influences the evolution of cooperation by varying the noise in detail.We find that the frequency of cooperators is closely related to the size of neighborhood and cost-to-benefit ratio r.In the case of lower r,the augmentation of k plays no positive role in promoting the cooperation as compared with that of k = 4,while for higher r the cooperation is improved for a growing size of neighborhood.At last,based on the above discussions,we explore the cluster-forming mechanism among the cooperators.The current results are beneficial to further understand the evolution of cooperation in many natural,social and biological systems.
基金Supported by the National Natural Science Foundation of China under Grant No.60904063Tianjin Municipal Natural Science Foundation under Grant No.11JCYBJC06600+1 种基金the Development Fund of Science and Technology for the Higher Education in Tianjin under Grant No.20090813the 7th Overseas Training Project for the Young and Middle Teachers in Tianjin Municipal Universities
文摘We combine the Fermi and Moran update rules in the spatial prisoner＇s dilemma and snowdrift games to investigate the behavior of collective cooperation among agents on the regular lattice. Large-scale simulations indicate that, compared to the model with only one update rule, the the role of update dynamics should be paid more attention in cooperation behavior exhibits the richer phenomena, and the evolutionary game theory. Meanwhile, we also observe that the introduction of Moran rule, which needs to consider all neighbor＇s information, can markedly promote the aggregate cooperation level, that is, randomly selecting the neighbor proportional to its payoff to imitate will facilitate the cooperation among agents. Current results will contribute to further understand the cooperation dynamics and evolutionary behaviors within many biological, economic and social systems.
