Skip to main content
Springer Nature Link
Log in

An analysis of the spatial prisoner’s dilemma using the partial differential equation

  • Original Article
  • Published:
Artificial Life and Robotics Aims and scope Submit manuscript

Abstract

We propose a partial differential equation that reproduces the behavior of a model that was constructed as one of the Prisoner’s Dilemma Games for mobility by Suzuki and Kimura in 2011. By numerical simulation of our equation connected on a lattice, it was shown that the equation reproduces the maintaining cooperation by oscillating the number of the game’s players like the previous study. We made a phase diagram, and we also found that depending on the parameters, the cooperative area had a comet pattern. We considered that the proposed equation reproduces the phenomenon and that the cooperative rate decreases as the rate of benefit increases, similar to previous results.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  1. Ale SB et al (2013) Evolution of cooperation: combining kin selection and reciprocal altruism into matrix games with social Dilemmas. PLoS One 8(5):e63761

    Article  Google Scholar 

  2. Suzuki S, Kimura H (2011) Osci llatory dynamics in the coevolution of cooperation and mobility. J Theor Biol 287:42–47

    Article  Google Scholar 

  3. Vainstein MH, Silva ATC, Arenzon JJ (2007) Does mobility decrease cooperation? J Theor Biol 244(4):722–728

    Article  MathSciNet  Google Scholar 

  4. Athena Aktipis C (2011) Is cooperation viable in mobile organisms? Simple walk away rule favors the evolution of cooperation in groups. Evol Hum Behav 32(4):263–276

    Article  Google Scholar 

  5. Capraro V, Jordan JJ, and Rand DG (2014) Cooperation increases with the benefit-to-cost ratio in one-shot Prisoner’s Dilemma experiments, SSRN: 2429862

  6. Mitra A et al (2018) The region of interest localization for glaucoma analysis from retinal fundus image using deep learning. Comput Methods Progr Biomed 165:25–35

    Article  Google Scholar 

Download references

Acknowledgements

Dr. Hiromichi Kimura and Dr. Hiroto Yonenoh were helpful in advising and discussing previous studies on PD and the SK model, so we especially thank them. This study was supported by Advanced Industrial Science and Technology(AIST), and TIA collaborative research program (Kakehashi).

Author information

Authors and Affiliations

  1. HIIRI, Advanced Industrial Science and Technology, Umezono 1-1-1 Central 2, Tsukuba, Ibaraki, Japan

    Masanori Shiro

  2. Takamatsu Information Technology, Takamatsu, Japan

    Yoshihide Kubo

Authors
  1. Masanori Shiro
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Yoshihide Kubo
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to Masanori Shiro.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Shiro, M., Kubo, Y. An analysis of the spatial prisoner’s dilemma using the partial differential equation. Artif Life Robotics 26, 91–96 (2021). https://doi.org/10.1007/s10015-020-00619-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10015-020-00619-1

Keywords