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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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    as
    1. John M. McNamara & Zoltan Barta & Lutz Fromhage & Alasdair I. Houston, 2008. "The coevolution of choosiness and cooperation," Nature, Nature, vol. 451(7175), pages 189-192, January.
    2. Xia, Chengyi & Wang, Juan & Wang, Li & Sun, Shiwen & Sun, Junqing & Wang, Jinsong, 2012. "Role of update dynamics in the collective cooperation on the spatial snowdrift games: Beyond unconditional imitation and replicator dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 45(9), pages 1239-1245.
    3. Xia, Cheng-yi & Ma, Zhi-qin & Wang, Zhen & Wang, Juan, 2012. "Evaluating fitness by integrating the highest payoff within the neighborhood promotes cooperation in social dilemmas," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(24), pages 6440-6447.
    4. Zhen Wang & Lin Wang & Zi-Yu Yin & Cheng-Yi Xia, 2012. "Inferring Reputation Promotes the Evolution of Cooperation in Spatial Social Dilemma Games," PLOS ONE, Public Library of Science, vol. 7(7), pages 1-9, July.
    5. Zhang, Haifeng & Yang, Hanxin & Du, Wenbo & Wang, Binghong & Cao, Xianbin, 2010. "Evolutionary public goods games on scale-free networks with unequal payoff allocation mechanism," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(5), pages 1099-1104.
    6. Francisco C Santos & Jorge M Pacheco & Tom Lenaerts, 2006. "Cooperation Prevails When Individuals Adjust Their Social Ties," PLOS Computational Biology, Public Library of Science, vol. 2(10), pages 1-8, October.
    7. Wang, Zhen & Du, Wen-Bo & Cao, Xian-Bin & Zhang, Lian-Zhong, 2011. "Integrating neighborhoods in the evaluation of fitness promotes cooperation in the spatial prisoner’s dilemma game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(7), pages 1234-1239.
    8. Zhang, Haifeng & Small, Michael & Yang, Hanxin & Wang, Binghong, 2010. "Adjusting learning motivation to promote cooperation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(21), pages 4734-4739.
    9. Markus Brede, 2013. "Short Versus Long Term Benefits and the Evolution of Cooperation in the Prisoner's Dilemma Game," PLOS ONE, Public Library of Science, vol. 8(2), pages 1-9, February.
    10. Matjaž Perc & Zhen Wang, 2010. "Heterogeneous Aspirations Promote Cooperation in the Prisoner's Dilemma Game," PLOS ONE, Public Library of Science, vol. 5(12), pages 1-8, December.
    11. C.-L. Tang & W.-X. Wang & X. Wu & B.-H. Wang, 2006. "Effects of average degree on cooperation in networked evolutionary game," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 53(3), pages 411-415, October.
    12. Christoph Hauert & Michael Doebeli, 2004. "Spatial structure often inhibits the evolution of cooperation in the snowdrift game," Nature, Nature, vol. 428(6983), pages 643-646, April.
    13. Dirk Helbing & Attila Szolnoki & Matjaž Perc & György Szabó, 2010. "Evolutionary Establishment of Moral and Double Moral Standards through Spatial Interactions," PLOS Computational Biology, Public Library of Science, vol. 6(4), pages 1-9, April.
    14. Xia, Cheng-yi & Ma, Zhi-qin & Wang, Yi-ling & Wang, Jin-song & Chen, Zeng-qiang, 2011. "Enhancement of cooperation in prisoner’s dilemma game on weighted lattices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(23), pages 4602-4609.
    15. A. Szolnoki & M. Perc, 2009. "Promoting cooperation in social dilemmas via simple coevolutionary rules," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 67(3), pages 337-344, February.
    16. M. Sysi-Aho & J. Saramäki & J. Kertész & K. Kaski, 2005. "Spatial snowdrift game with myopic agents," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 44(1), pages 129-135, March.
    17. Cheng-Yi Xia & Sandro Meloni & Yamir Moreno, 2012. "Effects Of Environment Knowledge On Agglomeration And Cooperation In Spatial Public Goods Games," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 15(supp0), pages 1-17.
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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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