School of Systems Science, Beijing Normal University, 100875 Beijing, China.
Chaos. 2022 Feb;32(2):023107. doi: 10.1063/5.0070358.
In evolutionary dynamics, the population structure and multiplayer interactions significantly impact the evolution of cooperation levels. Previous works mainly focus on the theoretical analysis of multiplayer games on regular networks or pairwise games on complex networks. Combining these two factors, complex networks and multiplayer games, we obtain the fixation probability and fixation time of the evolutionary public goods game in a structured population represented by a signed network. We devise a stochastic framework for estimating fixation probability with weak mistrust or strong mistrust mechanisms and develop a deterministic replicator equation to predict the expected density of cooperators when the system evolves to the equilibrium on a signed network. Specifically, the most interesting result is that negative edges diversify the cooperation steady state, evolving in three different patterns of fixed probability in Erdös-Rényi signed and Watts-Strogatz signed networks with the new "strong mistrust" mechanism.
在进化动力学中，群体结构和多方交互作用对合作水平的进化有重大影响。以前的工作主要集中在正则网络上的多方博弈或复杂网络上的成对博弈的理论分析上。将这两个因素——复杂网络和多方博弈结合起来，我们在一个由有符号网络表示的结构化群体中获得了进化公共物品博弈的固定概率和固定时间。我们设计了一个随机框架，用于估计具有弱不信任或强不信任机制的固定概率，并开发了一个确定性复制者方程，用于预测当系统在有符号网络上达到平衡时合作者的预期密度。具体来说，最有趣的结果是负边多样化了合作的稳定状态，在具有新的“强不信任”机制的 Erdös-Rényi 有符号网络和 Watts-Strogatz 有符号网络中，以三种不同的固定概率模式进化。
