Chinese Science Bulletin

, Volume 57, Issue 7, pp 724–728 | Cite as

Spatial prisoner’s dilemma games with increasing size of the interaction neighborhood on regular lattices

  • Juan Wang
  • ChengYi Xia
  • YiLing Wang
  • Shuai Ding
  • JunQing Sun
Open Access
Article Statistical Physics


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.


prisoner’s dilemma game emergence of cooperation size of interaction neighborhood 


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© The Author(s) 2012

Open Access This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

Authors and Affiliations

  • Juan Wang
    • 1
    • 2
  • ChengYi Xia
    • 1
    • 2
  • YiLing Wang
    • 3
  • Shuai Ding
    • 4
  • JunQing Sun
    • 1
    • 2
  1. 1.Tianjin Key Laboratory for Control Theory and Complicated Industry SystemsTianjin University of TechnologyTianjinChina
  2. 2.Key Laboratory of Computer Vision and System (Ministry of Education)Tianjin University of TechnologyTianjinChina
  3. 3.School of Life ScienceShanxi Normal UniversityLinfenChina
  4. 4.Institute of Computer Network SystemsHefei University of TechnologyHefeiChina

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