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Role of strategy update rules in the spatial memory-based mixed strategy games

  • Regular Article - Statistical and Nonlinear Physics
  • Published:
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Abstract

Based on a continuous mixed strategy game model considering the memory mechanism and the uncertainty of individual decision-making, we explore the influence of several different update rules on the spatial cooperation behavior. Here, we mainly investigate the role of the Moran-like process, Fermi rule and replicator dynamics in the evolution of cooperation. Meanwhile, we further compare the evolution of cooperation when the memory mechanism and individual uncertainty are taken into account. In particular, memory length M and strategy adjustment factor \(\delta \) can promote the cooperation behavior in different ways. Extensive Monte Carlo simulations indicate that the Moran-like process can generally drive the expansion of cooperative clusters faster and finally achieve the highest frequency of cooperation although the Fermi update rule performs better under the same condition. Moreover, the replicator dynamics create the worst scenario as far as the evolution of cooperation is concerned. Therefore, the level of cooperation strongly depends on the strategy update rules; these findings may be helpful to understand and analyze the evolutionary process of cooperation in many real-world natural and social systems.

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Data Availability Statement

This manuscript has no associated data or the data will not be deposited. [Authors’ comment: All data can be easily generated according to the procedure depicted in the text in Section 2.].

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Acknowledgements

This project is partially supported by the National Natural Science Foundation of China (NSFC) under Grant nos. 61773286 and 71401122. Li and Zhang are also thankful for the support of Tianjin graduate research and innovation project (under Grant 2019YJSB005).

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Authors and Affiliations

  1. Tianjin Key Laboratory for Control Theory and Complicated Industry Systems, Tianjin University of Technology, Tianjin, 300384, People’s Republic of China

    Fan Zhang, Juan Wang & Hongyu Gao

  2. School of Electrical and Electronic Engineering, Tianjin University of Technology, Tianjin, 300384, People’s Republic of China

    Fan Zhang, Juan Wang & Hongyu Gao

  3. Tianjin Key Laboratory of Intelligence Computing and Novel Software Technology, Tianjin University of Technology, Tianjin, 300384, People’s Republic of China

    Xiaopeng Li & Chengyi Xia

  4. Engineering Research Center of Learning-Based Intelligent System, Ministry of Education, Tianjin, 300384, People’s Republic of China

    Xiaopeng Li & Chengyi Xia

Authors
  1. Fan Zhang
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  2. Juan Wang
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  3. Hongyu Gao
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  4. Xiaopeng Li
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  5. Chengyi Xia
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Contributions

All the authors were involved in the preparation of the manuscript. All the authors have read and approved the final manuscript.

Corresponding authors

Correspondence to Juan Wang or Chengyi Xia.

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Zhang, F., Wang, J., Gao, H. et al. Role of strategy update rules in the spatial memory-based mixed strategy games. Eur. Phys. J. B 94, 22 (2021). https://doi.org/10.1140/epjb/s10051-020-00043-1

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  • DOI: https://doi.org/10.1140/epjb/s10051-020-00043-1

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