Evolution of cooperation and competition in multilayer networks

Cooperation and competition coexist and coevolve in natural and social systems. Cooperation generates resources, which in turn, drive non-cooperative competition to secure individual shares. How this complex interplay between cooperation and competition shapes the evolution of social dilemmas and welfare remains unknown. In this study, we introduce a two-layer evolutionary game model, in which one layer is a cooperative public goods game, and the other is a competitive involution game, with cross-layer feedback linking the two. We find that feedback can either promote or inhibit cooperation, depending on the baseline conditions. For example, moderate resource and synergy factor values can promote social welfare when feedback strength is large. This provides an approach to adjusting the strength and asymmetry of cross-layer feedback to promote cooperation and social welfare. We thus emphasize the importance of managing feedback mechanisms to balance cooperation and competition in complex social systems.