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Effect of Initial Fraction of Cooperators on Cooperative Behavior in Evolutionary Prisoner's Dilemma Game

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  • Keizo Shigaki
  • Zhen Wang
  • Jun Tanimoto
  • Eriko Fukuda

Abstract

We investigate the influence of initial fraction of cooperators on the evolution of cooperation in spatial prisoner's dilemma games. Compared with the results of heterogeneous networks, we find that there is a relatively low initial fraction of cooperators to guarantee higher equilibrium cooperative level. While this interesting phenomenon is contrary to the commonly shared knowledge that higher initial fraction of cooperators can provide better environment for the evolution of cooperation. To support our outcome, we explore the time courses of cooperation and find that the whole course can be divided into two sequent stages: enduring (END) and expanding (EXP) periods. At the end of END period, thought there is a limited number of cooperator clusters left for the case of low initial setup, these clusters can smoothly expand to hold the whole system in the EXP period. However, for high initial fraction of cooperators, superfluous cooperator clusters hinder their effective expansion, which induces many remaining defectors surrounding the cooperator clusters. Moreover, through intensive analysis, we also demonstrate that when the tendency of three cooperation cluster characteristics (cluster size, cluster number and cluster shape) are consistent within END and EXP periods, the state that maximizes cooperation can be favored.

Suggested Citation

  • Keizo Shigaki & Zhen Wang & Jun Tanimoto & Eriko Fukuda, 2013. "Effect of Initial Fraction of Cooperators on Cooperative Behavior in Evolutionary Prisoner's Dilemma Game," PLOS ONE, Public Library of Science, vol. 8(11), pages 1-7, November.
    • Handle: RePEc:plo:pone00:0076942
    DOI: 10.1371/journal.pone.0076942
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    References listed on IDEAS

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    Cited by:

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    3. Ping Zhu & Guiyi Wei, 2014. "Stochastic Heterogeneous Interaction Promotes Cooperation in Spatial Prisoner's Dilemma Game," PLOS ONE, Public Library of Science, vol. 9(4), pages 1-10, April.
    4. Jianguo Ren & Yonghong Xu, 2014. "Modelling the Effects of Selection Temperature and Mutation on the Prisoner’s Dilemma Game on a Complete Oriented Star," PLOS ONE, Public Library of Science, vol. 9(10), pages 1-9, October.
    5. Ding, Shuai & Wang, Juan & Ruan, Sumei & Xia, Chengyi, 2015. "Inferring to individual diversity promotes the cooperation in the spatial prisoner’s dilemma game," Chaos, Solitons & Fractals, Elsevier, vol. 71(C), pages 91-99.
    6. Ahsan Habib, Md. & Tanaka, Masaki & Tanimoto, Jun, 2020. "How does conformity promote the enhancement of cooperation in the network reciprocity in spatial prisoner's dilemma games?," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    7. Isabel Cristina Panziera Marques & Mário Franco, 2020. "Cooperation networks in the area of health: systematic literature review," Scientometrics, Springer;Akadémiai Kiadó, vol. 122(3), pages 1727-1750, March.
    8. Xu, Zhixiong & Xu, Zhehang & Zhang, Wei & Han, Xiao-Pu & Meng, Fanyuan, 2024. "Memory-based spatial evolutionary prisoner’s dilemma," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    9. Shu, Gang & Du, Xia & Li, Ya, 2016. "Surrounding information consideration promotes cooperation in Prisoner’s dilemma game," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 689-694.
    10. Wu-Jie Yuan & Cheng-Yi Xia, 2014. "Role of Investment Heterogeneity in the Cooperation on Spatial Public Goods Game," PLOS ONE, Public Library of Science, vol. 9(3), pages 1-6, March.
    11. Xie, Yunya & Bai, Yu & Zhang, Yankun & Peng, Zhengyin, 2024. "Trust-induced cooperation under the complex interaction of networks and emotions," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).

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