多元博弈中的溢出模式：合作的双刃效应及其协同进化
Spillover modes in multiplex games: double-edged effects on cooperation, and their coevolution
摘要：
近年来，人们越来越有兴趣研究多路网络上的游戏，这些游戏可以解释相关社交环境中的互动。然而，很少有人知道如何潜在的跨背景干扰，或溢出，个人的行为策略影响整体合作。我们认为三种合理的溢出模式，量化和比较其对合作的演变的影响。在我们的模型中，社交互动发生在两个网络层上：一个代表与网格中的近邻的重复互动，另一个代表与同一群体中随机个体的一次性互动。溢出可以发生在社会学习过程中，偶然的跨层策略转移，或在社会互动过程中，由于上下文干扰的实施错误。我们的分析结果，使用扩展的对近似，是在广泛的模拟很好的协议。我们发现溢出对合作的影响是双刃剑：如果某一层的合作受到青睐，那么增加溢出的强度可以促进合作，但是过多的溢出则是有害的。我们还发现了一个合作的双稳态现象：溢出阻碍或促进合作依赖于初始频率在每一层的合作。此外，比较策略组合，出现在每一个溢出模式提供了一个很好的指示，他们的共同进化动态与合作。我们的研究结果做出了可测试的预测，启发了未来的研究，并揭示了人类在社会领域的合作及其相互干扰。
英文摘要：
In recent years, there has been growing interest in studying games on multiplex networks that account for interactions across linked social contexts. However, little is known about how potential cross-context interference, or spillover, of individual behavioural strategy impact overall cooperation. We consider three plausible spillover modes, quantifying and comparing their effects on the evolution of cooperation. In our model, social interactions take place on two network layers: one represents repeated interactions with close neighbours in a lattice, the other represents one-shot interactions with random individuals across the same population. Spillover can occur during the social learning process with accidental cross-layer strategy transfer, or during social interactions with errors in implementation due to contextual interference. Our analytical results, using extended pair approximation, are in good agreement with extensive simulations. We find double-edged effects of spillover on cooperation: increasing the intensity of spillover can promote cooperation provided cooperation is favoured in one layer, but too much spillover is detrimental. We also discover a bistability phenomenon of cooperation: spillover hinders or promotes cooperation depending on initial frequencies of cooperation in each layer. Furthermore, comparing strategy combinations that emerge in each spillover mode provides a good indication of their co-evolutionary dynamics with cooperation. Our results make testable predictions that inspire future research, and sheds light on human cooperation across social domains and their interference with one another.
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