In social dilemmas under weak selection, the capacity for a player to exhibit updating passivity or interact with its own strategy can lead to conflicting outcomes. The central question is which effect is stronger and how their simultaneous presence influences the evolution of cooperation. We introduce a model that considers both effects using different weight factors. We derive theoretical solutions for the conditions of cooperation success and the cooperation level under weak selection, scanning the complete parameter space. When the weight factors are equally strong, the promoting effect of self-interaction to cooperation surpasses the inhibitory effect of updating passivity. Intriguingly, however, we identify non-monotonous cooperation-supporting effects when the weight of updating passivity increases more rapidly. Our findings are corroborated by Monte Carlo simulations and demonstrate robustness across various game types, including the prisoner's dilemma, stag-hunt, and snowdrift games.

翻译：在弱选择下的社会困境中，参与者展现更新被动性或与自身策略互动可能导致相互冲突的结果。核心问题在于哪种效应更强，以及它们的同时存在如何影响合作的演化。我们引入一个模型，通过不同权重因子同时考虑这两种效应。我们推导出弱选择下合作成功条件与合作水平的理论解，并扫描完整参数空间。当权重因子强度相等时，自相互作用对合作的促进作用超过更新被动性的抑制作用。然而有趣的是，我们发现当更新被动性的权重增长更快时，会产生非单调的合作促进效应。我们的研究结果经蒙特卡洛模拟验证，并在包括囚徒困境、猎鹿博弈和雪堆博弈等多种博弈类型中展现出鲁棒性。