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

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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.

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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).

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Correspondence to Masanori Shiro.

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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

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

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