In a population of interacting individuals, the environment for interactions often changes due to individuals’ behaviors, which in turn drive the evolution of individuals’ behaviors. The interplay between the environment and individuals’ behaviors has been demonstrated to remarkably influence the evolutionary outcomes. In reality, in highly cognitive species such as social primates and human beings, individuals are often capable of perceiving the environment change and then differentiate their strategies across different environment states. We propose a model of environmental feedback with state-dependent strategies: individuals have perceptions of distinct environment states and therefore take distinct sub-strategies under each of them; based on the sub-strategy, individuals then decide their behaviors; their behaviors subsequently modify the environment state. We use the theory of stochastic games and evolutionary dynamics to analyze this idea. We find that when environment changes slower than behaviors, state-dependent strategies (i.e. taking different sub-strategies under different environment states) can outperform state-independent strategies (i.e. taking an identical sub-strategy under all environment states), such as Win-Stay, Lose-Shift, the most leading strategy among state-independent strategies. The intuition is that delayed environmental feedback provides chances for individuals with state-dependent strategies to exploit those with state-independent strategies. Our results hold (1) in both well-mixed and structured populations; (2) when the environment switches between two or more states. Furthermore, the environment changing rate decides if state-dependent strategies benefit global cooperation. The evolution sees the rise of the cooperation level for fast environment switching and the decrease otherwise. Our work stresses that individuals’ perceptions of different environment states are beneficial to their survival and social prosperity in a changing world.

在交互的个体群体中，交互的环境往往会因个体的行为而改变，进而推动个体行为的演化。环境和个人行为之间的相互作用已被证明显着影响进化结果。实际上，在社会灵长类动物和人类等高度认知的物种中，个体通常能够感知环境变化，然后在不同的环境状态下区分他们的策略。我们提出了一个具有状态依赖策略的环境反馈模型：个体对不同的环境状态有感知，因此在每个状态下采取不同的子策略；基于子策略，个人然后决定他们的行为；他们的行为随后会改变环境状态。我们使用随机博弈和进化动力学理论来分析这个想法。我们发现当环境变化比行为慢时，状态依赖策略（即在不同环境状态下采取不同的子策略）可以优于状态无关策略（即在所有环境状态下采取相同的子策略），例如 Win- Stay, Lose-Shift，状态独立策略中最领先的策略。直觉是，延迟的环境反馈为具有状态依赖策略的个体提供了利用具有状态独立策略的个体的机会。我们的结果（1）在混合良好和结构化的人群中都成立；(2) 当环境在两个或多个状态之间切换时。此外，环境变化率决定依赖国家的战略是否有利于全球合作。演进过程中，快速环境切换的合作水平上升，否则合作水平下降。我们的工作强调，个人对不同环境状态的看法有利于他们在不断变化的世界中的生存和社会繁荣。