Spatial prisoner’s dilemma games with increasing size of the interaction neighborhood on regular lattices |
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Authors: | Juan Wang ChengYi Xia YiLing Wang Shuai Ding JunQing Sun |
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Institution: | Key Laboratory for Control Theory and Complicated Industry Systems, Tianjin University of Technology, Tianjin 300384, China; 2 Key Laboratory of Computer Vision and System (Ministry of Education), Tianjin University of Technology, Tianjin 300384, China; 3 School of Life Science, Shanxi Normal University, Linfen 041000, China; 4 Institute of Computer Network Systems, Hefei University of Technology, Hefei 230009, China |
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Abstract: | 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. |
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Keywords: | prisoner's dilemma game emergence of cooperation size of interaction neighborhood |
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