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Oscillation and burst transition of human cooperation

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Abstract

The oscillation of competing species is especially important for maintaining biodiversity. However, there has long been little evidence of oscillation in two-strategy games. Here we address this problem by studying a social-norm-driven probabilistic migration model where the movement of agents is determined by widespread conformity and self-centered inequity aversion norms. Non-trivially, we observe a tide-like burst as well as burst transition of cooperation that has been rarely discovered in the prisoner’s dilemma before, where the dynamically generated oscillation of competing strategies does not require bridging of any transition states or transition strategies, thus defining a novel oscillating behavior fundamentally different from the conventional cyclic dominance previously found in a game of at least three or more strategies. Although in most cases an explicit adherence to either of the above two norms can sustain cooperation alone, the best outcome always comes from their synergy. This is mainly because conformity norm, as a manifestation of group wisdom, is often a reliable stabilizer of the thriving of cooperation. Besides, it shows that dilemma strength as well as noise plays an important role in altering oscillating behavior. In particular, a slow increase in noise amplitude can cause the burst of cooperation to traverse a closed loop, for instance, from steady to tide-like and back to steady, reflecting an interesting and unusual dynamic property. In addition, there exists a noise threshold beyond which it is possible for an explosion of cooperation. Our results highlight the importance of social norms in the burst transition of human cooperation and add evidence for oscillation in two-strategy games.

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Data availability

The datasets generated during the current study are available from the corresponding author on reasonable request.

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Acknowledgements

Z. Yang acknowledges the support from National Natural Science Foundation of China (NSFC) under Grant No. 61703323. Z. Li acknowledges the support from NSFC under Grant No. 61673310.

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  1. Center for Complex Intelligent Networks, School of Mechano-electronic Engineering, Xidian University, Xi’an, 710071, China

    Zhihu Yang & Zhi Li

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  1. Zhihu Yang
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  2. Zhi Li
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Correspondence to Zhihu Yang.

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Yang, Z., Li, Z. Oscillation and burst transition of human cooperation. Nonlinear Dyn 108, 4599–4610 (2022). https://doi.org/10.1007/s11071-022-07376-9

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  • DOI: https://doi.org/10.1007/s11071-022-07376-9

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