As an important part of the evolution of cooperation, interaction diversity has attracted extensive attention. Traditional studies mainly focus exclusively on either time or space, and the comprehensive impact of these two dimensions on the evolution of cooperation deserves further exploration. In this paper, the interaction willingness is abstracted as the network weight, and an adaptive mechanism for interaction willingness based on the delay effect is proposed by combining the network weight and accumulated payoff. Specifically, individuals adjust their willingness to participate in the game with a delay, considering the change in accumulated payoffs within a certain period, rather than the change in immediate payoffs. The degree of delay is reflected in the length of individuals' memory of historical payoffs. Simulation results deviate from the intuition that more information facilitates cooperation, and in certain modes of interaction willingness adjustment, the correlation between cooperation level and memory–length is non–monotonic. Long–memory is conducive to promoting cooperation under the condition of a relatively large range adjustment of interaction willingness. Conversely, with a narrow adjustment range of interaction willingness, cooperation can be effectively established with short–memory. These results hold substantial implications for both theory and practice, as slight adjustment often corresponds to low loss and high operability. In addition, the underlying mechanism is furthermore explored, revealing that the ‘isolation zones’ composed of individuals with low interaction willingness play an important role in promoting cooperation.

中文翻译：

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基于记忆的适应性交互意愿增强空间囚徒困境中的合作


作为合作演进的重要组成部分，互动多样性受到广泛关注。传统研究主要集中在时间或空间上，这两个维度对合作演化的综合影响值得进一步探讨。本文将交互意愿抽象为网络权重，结合网络权重和累积收益提出了一种基于延迟效应的交互意愿自适应机制。具体来说，个体延迟参与博弈的意愿调整是考虑一定时期内累积收益的变化，而不是即时收益的变化。延迟的程度反映在个人对历史收益的记忆长度上。模拟结果偏离了更多信息促进合作的直觉，并且在某些交互意愿调整模式下，合作水平与记忆长度之间的相关性是非单调的。长记忆有利于在互动意愿调整幅度较大的情况下促进合作。反之，交互意愿调整范围窄，短记忆可以有效建立合作。这些结果对理论和实践都具有重大意义，因为轻微的调整通常对应于低损耗和高可操作性。此外，还进一步探讨了其背后的机制，揭示了由低互动意愿个体组成的“隔离区”在促进合作方面发挥着重要作用。