Abstract Group interactions, formulated in terms of a public goods game, can not be deduced by the corresponding sum of pairwise interactions. This study proposes a collective interdependence characterizing the functioning of interdependent groups between subnetworks. Via the establishment of global group interactions across subnetwork layers, we show a double-edged sword of collective interdependence in promoting cooperation. Enhancement of collective interdependence hinders the evolution of cooperation whenever global synergy factor is small, while an optimal collective interdependence emerges most favoring the evolution of cooperation for high global synergy factors. However, for such high global synergy factors a low level of interdependence puts cooperators to a most disadvantaged place. A combination of low levels of collective interdependence and high local synergy factors shows that a moderate global synergetic effect most favors the evolution of cooperation. Our work reveals that collective interdependence impacts interdependent network reciprocity significantly and highlights the importance of network reciprocity in enhancing the evolution of cooperation.

中文翻译：

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由多层网络上的集体相互依赖驱动的合作演变

摘要 以公共物品博弈形式表述的群体相互作用不能由相应的成对相互作用的总和推导出来。本研究提出了一种集体相互依存关系，表征了子网之间相互依存组的功能。通过建立跨子网层的全局组交互，我们展示了促进合作的集体相互依赖的双刃剑。当全球协同因素较小时，集体相互依存的增强阻碍了合作的演化，而最优集体相互依存的出现最有利于全球协同因素高的合作演化。然而，对于如此高的全球协同因素，低水平的相互依存使合作者处于最不利的位置。低水平的集体相互依存和高水平的局部协同因素的结合表明，适度的全球协同效应最有利于合作的演变。我们的工作表明，集体相互依存显着影响相互依存的网络互惠，并强调了网络互惠在促进合作演变方面的重要性。