标题： 多层网络中合作与竞争的演变 显示英文标题

标题： Evolution of cooperation and competition in multilayer networks

摘要： 合作与竞争在自然和社会系统中共存并共同进化。合作产生资源，这些资源反过来驱动非合作竞争以确保个体份额。这种合作与竞争之间的复杂相互作用如何塑造社会困境和福利的发展仍然未知。在本研究中，我们引入了一个双层演化博弈模型，在该模型中一层是一个合作公共品博弈，另一层是一个竞争性反演博弈，并且通过跨层反馈将两者联系起来。我们发现，反馈可以促进或抑制合作，这取决于基线条件。例如，当反馈强度较大时，适度的资源和协同因子值可以促进社会福利。这提供了一种调整跨层反馈的强度和不对称性的方法来促进合作和社会福利。因此，我们强调管理反馈机制以平衡复杂社会系统中的合作和竞争的重要性。 显示英文摘要

摘要： 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.