论文标题
在网络上合作演变的扰动理论
Perturbation theory for evolution of cooperation on networks
论文作者
论文摘要
网络结构是促进社会困境游戏合作的机制。在本研究中，我们探索图形手术，即，略微扰动给定的网络，朝着更好地培养合作的网络。为此，我们开发了一种扰动理论，以评估合作倾向的变化，当我们添加或从给定网络中删除单个边缘时。我们的扰动理论是针对先前提出的基于随机步行的理论，该理论提供了阈值益处与成本的比率，$（b/c）^*$，这是捐赠游戏中收益与成本比率的价值，在上面的捐赠游戏中，合作者比在任何有限网络中更可能固定合作者。我们发现，当我们在大多数情况下删除单个边缘时，$（b/c）^*$会减少，并且我们的扰动理论以合理的精度捕获，而边缘删除会使$（b/c）^*$ small small small small small。相反，当我们增加边缘时，$（b/c）^*$倾向于增加，并且摄动理论不擅长预测大量$（b/c）^*$的边缘添加。我们的扰动理论大大降低了计算图手术结果的计算复杂性。
Network structure is a mechanism for promoting cooperation in social dilemma games. In the present study, we explore graph surgery, i.e., to slightly perturb the given network, towards a network that better fosters cooperation. To this end, we develop a perturbation theory to assess the change in the propensity of cooperation when we add or remove a single edge to/from the given network. Our perturbation theory is for a previously proposed random-walk-based theory that provides the threshold benefit-to-cost ratio, $(b/c)^*$, which is the value of the benefit-to-cost ratio in the donation game above which the cooperator is more likely to fixate than in a control case, for any finite networks. We find that $(b/c)^*$ decreases when we remove a single edge in a majority of cases and that our perturbation theory captures at a reasonable accuracy which edge removal makes $(b/c)^*$ small to facilitate cooperation. In contrast, $(b/c)^*$ tends to increase when we add an edge, and the perturbation theory is not good at predicting the edge addition that changes $(b/c)^*$ by a large amount. Our perturbation theory significantly reduces the computational complexity for calculating the outcome of graph surgery.
