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We studied the evolution of cooperation in the prisoner’s dilemma game on a square lattice where the size of the interaction neighborhood is considered. Firstly, the effects of noise and the cost-to-benefit ratio on the maintenance of cooperation were investigated. The results indicate that the cooperation frequency depends on the noise and cost-to-benefit ratio: cooperation reaches a climax as noise increases, but it monotonously decreases and even vanishes with the ratio increasing. Furthermore, we investigated how the size of the interaction neighborhood affects the emergence of cooperation in detail. Our study demonstrates that cooperation is remarkably enhanced by an increase in the size of the interaction neighborhood. However, cooperation died out when the size of the interaction neighborhood became too large since the system was similar to the mean-field system. On this basis, a cluster-forming mechanism acting among cooperators was also explored, and it showed that the moderate range of the neighborhood size is beneficial for forming larger cooperative clusters. Finally, large-scale Monte Carlo simulations were carried out to visualize and interpret these phenomena explicitly.
The studied of evolution of cooperation in the prisoner’s dilemma game on a square lattice where the size of the interaction neighborhood was considered. The results of noise and the cost-to-benefit ratio on the maintenance of cooperation were investigated. that the cooperation frequency depends on the noise and cost-to-benefit ratio: cooperation reaches a climax as noise increases, but but monotonously reduce and even vanishes with the ratio increase. of cooperation in detail in the size of the interaction neighborhood. However, cooperation died out when the size of the interaction of has been too large since the system was similar to the mean-field system . On this basis, a cluster-forming mechanism acting among cooperators was also explored, and it showed that the moderat Finally, large-scale Monte Carlo simulations were carried out to visualize and interpret these phenomena explicitly.