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Emergence of cooperation promoted by higher-order strategy updates

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  • Dini Wang
  • Peng Yi
  • Yiguang Hong
  • Jie Chen
  • Gang Yan

Abstract

Cooperation is fundamental to human societies, and the interaction structure among individuals profoundly shapes its emergence and evolution. In real-world scenarios, cooperation prevails in multi-group (higher-order) populations, beyond just dyadic behaviors. Despite recent studies on group dilemmas in higher-order networks, the exploration of cooperation driven by higher-order strategy updates remains limited due to the intricacy and indivisibility of group-wise interactions. Here we investigate four categories of higher-order mechanisms for strategy updates in public goods games and establish their mathematical conditions for the emergence of cooperation. Such conditions uncover the impact of both higher-order strategy updates and network properties on evolutionary outcomes, notably highlighting the enhancement of cooperation by overlaps between groups. Interestingly, we discover that the group-mutual comparison update – selecting a high-fitness group and then imitating a random individual within this group – can prominently promote cooperation. Our analyses further unveil that, compared to pairwise interactions, higher-order strategy updates generally improve cooperation in most higher-order networks. These findings underscore the pivotal role of higher-order strategy updates in fostering collective cooperation in complex social systems.Author summary: Human societies often organize and cooperate within social groups, where relatives, friends, neighbors, and colleagues influence behavior at both group and individual levels. Individuals may exhibit biased or neutral attitudes when selecting a neighboring group and then a peer within it for imitation or comparison, a process termed as higher-order strategy update. These selection preferences originate from four personality types: aggressive, open-minded, myopic, and passive. This work demonstrates that the open-minded type – indiscriminately imitating a peer within a well-performing group – significantly promotes cooperation. The mathematical framework proposed in this study deepens the understanding of how decision-making within higher-order structures affects the emergence and spread of cooperative behaviors.

Suggested Citation

  • Dini Wang & Peng Yi & Yiguang Hong & Jie Chen & Gang Yan, 2025. "Emergence of cooperation promoted by higher-order strategy updates," PLOS Computational Biology, Public Library of Science, vol. 21(8), pages 1-21, August.
    • Handle: RePEc:plo:pcbi00:1012891
    DOI: 10.1371/journal.pcbi.1012891
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    2. Martin A. Nowak & Akira Sasaki & Christine Taylor & Drew Fudenberg, 2004. "Emergence of cooperation and evolutionary stability in finite populations," Nature, Nature, vol. 428(6983), pages 646-650, April.
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