Abstract

We propose a novel dynamic link weight adjustment model, in which link weights on static network will be dynamically adjusted according to agents’ influence during the evolutionary process. To be specific, when an agent’s strategy is learned by one of his direct neighbors, his influence will be expanded by one unit \(\beta \). Then link weights between agents will be adaptively adjusted by counting the influence of agents. Meanwhile, we utilize a variable \(\delta \) to control the range of link weights, that is, link weights can only be limited within the interval \([1-\delta ,1+\delta ]\). In our model, it should be noted that link weights between agents will be integrated into the fitness calculation process. Through abundant simulations, the results indicate that the newly proposed model can significantly foster the persistence and emergence of cooperation. In addition, when the cost-to-benefit ratio u is quite small, the level of cooperation will increase with the augmentation of \(\delta \). However, when the cost-to-benefit ratio u exceeds a certain value, the level of cooperation increases at the early stage and then decreases with the growth of \(\delta \). As for the potential reasons, we observe that it is closely related to the type of connections, in which the cooperation can flourish once \(C-C\) type links dominate the system, while other types will hamper the evolution of cooperation. Taking together, the current model and results will provide some insights into the collective cooperation within the human population.

Graphic abstract

We propose a novel dynamic link weight adjustment model, in which link weights on static network will be dynamically adjusted according to agents’ influence during the evolutionary process. In this figure, the color phase encodes the frequency of cooperation \(\rho \)C on \(\delta -\varDelta \) parameter plane for a series values of cost-to-benefit ratio u. Panels (a) to (f) are obtained at the cost-to-benefit ratio u=0.01, u=0.015, u=0.02, u=0.025, u=0.03, and u=0.035, respectively. It can be found that when u is quite small, the level of cooperation increases with the augmentation of \(\delta \), while the parameter \(\varDelta \) seems to have no significant impact on the evolution of cooperation. Similar with previous discussion, when the cost-to-benefit ratio u exceeds to a certain value, the level of cooperation presents the first increase and then decrease with the increase of \(\delta \). In addition, when the parameter \(\delta \) reaches a certain value, the level of cooperation decreases as \(\varDelta \) gradually grows. All these observations suggest that there is an optimal combination \(\delta -\varDelta \) promoting the evolution of cooperation. All results are obtained at L=100, MCS=\(3\times 10^4, \beta =1\) and K=0.1.

中文翻译：

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影响力引起的动态链接权重调整在空间囚徒困境博弈合作中的作用

摘要

我们提出了一种新颖的动态链路权重调整模型，该模型将根据代理在进化过程中的影响来动态调整静态网络上的链路权重。具体来说，当一个代理人的策略被他的一个直接邻居学习时，他的影响力将扩大一个单位\（\ beta \）。然后，将通过计算代理的影响来自适应地调整代理之间的链接权重。同时，我们利用变量\（\ delta \）来控制链接权重的范围，也就是说，链接权重只能限制在区间\（[1- \ delta，1 + \ delta] \）。在我们的模型中，应该注意的是，代理之间的链接权重将被整合到适应度计算过程中。通过大量的仿真，结果表明新提出的模型可以极大地促进合作的持久性和出现。另外，当成本效益比u很小时，合作程度会随着\（\ delta \）的增加而增加。但是，当成本效益比u超过某个值时，合作水平在早期阶段增加，然后随着\（\ delta \）的增加而降低。至于潜在的原因，我们观察到它与联系的类型密切相关，在这种联系中，合作可以蓬勃发展。\（CC \）类型的链接主导着系统，而其他类型的链接则阻碍了合作的发展。综上所述，当前的模式和结果将为人们内部的集体合作提供一些见识。

图形摘要

我们提出了一种新颖的动态链路权重调整模型，该模型将根据代理在进化过程中的影响来动态调整静态网络上的链路权重。在该图中，彩色相位在\（\ delta-\ varDelta \）参数平面上编码协作频率\（\ rho \） C以获得一系列成本效益比u。分别以成本效益比u = 0.01，u = 0.015，u = 0.02，u = 0.025，u = 0.03和u = 0.035获得面板（a）至（f）。可以发现，当你很小，合作程度随\（\ delta \）的增加而增加，而参数\（\ varDelta \）似乎对合作的演变没有显着影响。与先前的讨论类似，当成本效益比u超过一定值时，合作程度呈现出先增加后减少的趋势，随着\（\ delta \）的增加而降低。另外，当参数\（\ delta \）达到某个值时，随着\（\ varDelta \）逐渐增长，协作程度降低。所有这些观察结果表明存在一个最佳组合\（\ delta-\ varDelta \）促进合作的发展。所有结果都是在L = 100，MCS = \（3 × 10 ^ 4，\ beta = 1 \）和K = 0.1的情况下获得的。