Interaction between populations promotes cooperation in voluntary prisoner's dilemma

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Juan Shi, Die Hu, Rui Tao, Yunchen Peng, Yong Li, Jinzhuo Liu

Published: 2021, Last Modified: 03 Aug 2025Appl. Math. Comput. 2021EveryoneRevisionsBibTeXCC BY-SA 4.0
Abstract: Highlights•A fascinating spiral pattern is spontaneously formed, adding a new population always brings additional prey to cooperators in other populations, leading to competing spatial dynamics and pattern formation.•The inherent cyclic dominance of the strategies results in the self-organization of populations on the square lattice and ultimately effectively promotes cooperation.•The cooperation facilitation mechanism depends on the spontaneous emergence of the dynamically accelerating invasion processes. Through these processes, unlike defectors, significant evolutionary advantages are created for cooperators.