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Direct Reciprocity in Spatial Populations Enhances R-Reciprocity As Well As ST-Reciprocity

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  • Kohei Miyaji
  • Jun Tanimoto
  • Zhen Wang
  • Aya Hagishima
  • Naoki Ikegaya

Abstract

As is well-known, spatial reciprocity plays an important role in facilitating the emergence of cooperative traits, and the effect of direct reciprocity is also obvious for explaining the cooperation dynamics. However, how the combination of these two scenarios influences cooperation is still unclear. In the present work, we study the evolution of cooperation in 2×2 games via considering both spatial structured populations and direct reciprocity driven by the strategy with 1-memory length. Our results show that cooperation can be significantly facilitated on the whole parameter plane. For prisoner's dilemma game, cooperation dominates the system even at strong dilemma, where maximal social payoff is still realized. In this sense, R-reciprocity forms and it is robust to the extremely strong dilemma. Interestingly, when turning to chicken game, we find that ST-reciprocity is also guaranteed, through which social average payoff and cooperation is greatly enhanced. This reciprocity mechanism is supported by mean-field analysis and different interaction topologies. Thus, our study indicates that direct reciprocity in structured populations can be regarded as a more powerful factor for the sustainability of cooperation.

Suggested Citation

  • Kohei Miyaji & Jun Tanimoto & Zhen Wang & Aya Hagishima & Naoki Ikegaya, 2013. "Direct Reciprocity in Spatial Populations Enhances R-Reciprocity As Well As ST-Reciprocity," PLOS ONE, Public Library of Science, vol. 8(8), pages 1-8, August.
    • Handle: RePEc:plo:pone00:0071961
    DOI: 10.1371/journal.pone.0071961
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    Cited by:

    1. 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.
    2. Niu, He & Chen, Yuyou & Ye, Hang & Zhang, Hong & Li, Yan & Chen, Shu, 2020. "Distinguishing punishing costly signals from nonpunishing costly signals can facilitate the emergence of altruistic punishment," Applied Mathematics and Computation, Elsevier, vol. 371(C).
    3. 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.
    4. Huang, Shasha & Luo, Dang, 2015. "Impact of separation of interaction and replacement neighborhoods on spatial reciprocity," Applied Mathematics and Computation, Elsevier, vol. 253(C), pages 318-323.

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