The College of Artificial Intelligence, Southwest University, No.2 Tiansheng Road, Beibei, Chongqing 400715, China.
School of Public Policy and Administration, Chongqing University, No.174 Shazhengjie, Shapingba, Chongqing 400044, China.
Chaos. 2022 Jul;32(7):073118. doi: 10.1063/5.0099444.
In the evolution of cooperation, the individuals' payoffs are commonly random in real situations, e.g., the social networks and the economic regions, leading to unpredictable factors. Therefore, there are chances for each individual to obtain the exceeding payoff and risks to get the low payoff. In this paper, we consider that each individual's payoff follows a specific probability distribution with a fixed expectation, where the normal distribution and the exponential distribution are employed in our model. In the simulations, we perform the models on the weak prisoner's dilemmas (WPDs) and the snowdrift games (SDGs), and four types of networks, including the hexagon lattice, the square lattice, the small-world network, and the triangular lattice are considered. For the individuals' normally distributed payoff, we find that the higher standard deviation usually inhibits the cooperation for the WPDs but promotes the cooperation for the SDGs. Besides, with a higher standard deviation, the cooperation clusters are usually split for the WPDs but constructed for the SDGs. For the individuals' exponentially distributed payoff, we find that the small-world network provides the best condition for the emergence of cooperators in WPDs and SDGs. However, when playing SDGs, the small-world network allows the smallest space for the pure cooperative state while the hexagon lattice allows the largest.
在合作的演变中，个体的收益在现实情况下通常是随机的，例如社交网络和经济区域，这导致了不可预测的因素。因此，每个个体都有机会获得超额收益，也有机会获得低收益。在本文中，我们假设每个个体的收益遵循特定的概率分布，具有固定的期望，其中我们的模型采用了正态分布和指数分布。在模拟中，我们在弱囚徒困境（WPDs）和雪堆博弈（SDGs）上执行模型，并考虑了四种网络，包括六边形晶格、正方形晶格、小世界网络和三角形晶格。对于个体的正态分布收益，我们发现较高的标准差通常会抑制 WPDs 的合作，但会促进 SDGs 的合作。此外，随着标准差的增加，WPDs 的合作簇通常会分裂，但 SDGs 的合作簇会构建。对于个体的指数分布收益，我们发现小世界网络为 WPDs 和 SDGs 中合作者的出现提供了最佳条件。然而，在玩 SDGs 时，小世界网络允许合作者的纯合作状态的空间最小，而六边形晶格允许的空间最大。
