Yang Han-Xin, Wang Wen-Xu, Wu Zhi-Xi, Lai Ying-Cheng, Wang Bing-Hong
Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China.
Phys Rev E Stat Nonlin Soft Matter Phys. 2009 May;79(5 Pt 2):056107. doi: 10.1103/PhysRevE.79.056107. Epub 2009 May 19.
We propose a strategy for achieving maximum cooperation in evolutionary games on complex networks. Each individual is assigned a weight that is proportional to the power of its degree, where the exponent alpha is an adjustable parameter that controls the level of diversity among individuals in the network. During the evolution, every individual chooses one of its neighbors as a reference with a probability proportional to the weight of the neighbor, and updates its strategy depending on their payoff difference. It is found that there exists an optimal value of alpha, for which the level of cooperation reaches maximum. This phenomenon indicates that, although high-degree individuals play a prominent role in maintaining the cooperation, too strong influences from the hubs may counterintuitively inhibit the diffusion of cooperation. Other pertinent quantities such as the payoff, the cooperator density as a function of the degree, and the payoff distribution are also investigated computationally and theoretically. Our results suggest that in order to achieve strong cooperation on a complex network, individuals should learn more frequently from neighbors with higher degrees, but only to a certain extent.
我们提出了一种在复杂网络上的进化博弈中实现最大合作的策略。为每个个体分配一个与其度的幂成正比的权重，其中指数α是一个可调节参数，用于控制网络中个体之间的多样性水平。在进化过程中，每个个体以与其邻居权重成正比的概率选择其邻居之一作为参考，并根据它们的收益差异更新其策略。研究发现，存在一个α的最优值，此时合作水平达到最大值。这一现象表明，尽管高度数个体在维持合作方面发挥着突出作用，但来自枢纽节点的影响过强可能会出人意料地抑制合作的传播。还通过计算和理论研究了其他相关量，如收益、作为度的函数的合作者密度以及收益分布。我们的结果表明，为了在复杂网络上实现强大的合作，个体应该更频繁地向度数较高的邻居学习，但只能在一定程度上。
