Szolnoki Attila, Perc Matjaz
Research Institute for Technical Physics and Materials Science, PO Box 49, H-1525 Budapest, Hungary.
Phys Rev E Stat Nonlin Soft Matter Phys. 2010 May;81(5 Pt 2):057101. doi: 10.1103/PhysRevE.81.057101. Epub 2010 May 4.
We study the evolution of cooperation under the assumption that the collective benefits of group membership can only be harvested if the fraction of cooperators within the group, i.e., their critical mass, exceeds a threshold value. Considering structured populations, we show that a moderate fraction of cooperators can prevail even at very low multiplication factors if the critical mass is minimal. For larger multiplication factors, however, the level of cooperation is highest at an intermediate value of the critical mass. The latter is robust to variations of the group size and the interaction network topology. Applying the optimal critical mass threshold, we show that the fraction of cooperators in public goods games is significantly larger than in the traditional linear model, where the produced public good is proportional to the fraction of cooperators within the group.
只有当群体中合作者的比例，即其临界质量，超过一个阈值时，群体成员的集体利益才能实现。考虑结构化种群，我们表明，如果临界质量最小，即使在非常低的繁殖因子下，适度比例的合作者也能占优势。然而，对于较大的繁殖因子，合作水平在临界质量的中间值时最高。后者对于群体规模和交互网络拓扑结构的变化具有鲁棒性。应用最优临界质量阈值，我们表明公共物品博弈中合作者的比例显著大于传统线性模型中的比例，在传统线性模型中，所产生的公共物品与群体中合作者的比例成正比。
