Evolution of cooperation driven by collective interdependence on multilayer networks

•The effects of collective interdependence on the evolution of cooperation are studied.•Global and local synergetic effects affect the evolution of cooperation significantly.•A moderate collective interdependence facilitates the propagation of cooperation best.•Collective interdependence is a double-edged sword in promoting cooperation.•The effects of collective interdependence impact network reciprocity significantly. 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.