Wu Te, Fu Feng, Zhang Yanling, Wang Long
Center for Systems and Control, State Key Laboratory for Turbulence and Complex Systems, College of Engineering, Peking University, Beijing 100871, China.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Jun;85(6 Pt 2):066104. doi: 10.1103/PhysRevE.85.066104. Epub 2012 Jun 6.
"Voting with feet" describes the prominent social phenomenon that people tend to move away from deteriorating neighborhoods and search for and join prosperous groups. To quantify the role this kind of expectation-driven migration plays in the evolution of cooperation, here we study a simple yet effective model of cooperation based on spatial public goods games. The population structure is characterized by a square lattice with some nodes being left empty. Individuals have expectations toward their current habitats. Dissatisfied players, whose expectation is not met after interacting with all directly connected neighbors, tend to abstain from the groups of low quality by moving away and explore the physical niches of avail. How fast interaction happens relatively to selection is regulated by the time-scale ratio of game interaction to natural selection. Under strong selection, simulation results show that cooperation is greatly improved for either low, moderate, or high expectations compared to whenever the expectation-driven migration is absent. Further explorations reveal that neither too high nor too low but rather a combination of moderate expectations and rapid interaction establishes cooperation for a moderate public goods enhancement factor. There exists an optimal interval of expectation level most favoring the evolution of cooperation as the required time-scale ratio is minimized.
“用脚投票”描述了一种显著的社会现象，即人们倾向于搬离环境恶化的社区，去寻找并加入繁荣的群体。为了量化这种预期驱动的迁移在合作演化中所起的作用，我们在此研究一个基于空间公共品博弈的简单而有效的合作模型。种群结构由一个有一些节点为空的方形晶格表征。个体对其当前栖息地有预期。那些在与所有直接相连的邻居互动后预期未得到满足的不满意玩家，倾向于通过离开来脱离低质量群体，并探索可用的物理生态位。互动相对于选择发生的速度由博弈互动与自然选择的时间尺度比来调节。在强选择下，模拟结果表明，与不存在预期驱动的迁移时相比，对于低、中或高预期，合作都有很大改善。进一步的探索表明，既不是过高也不是过低，而是适度预期和快速互动的结合，才能在公共品增强因子适中时建立合作。当所需的时间尺度比最小时，存在一个最有利于合作演化的期望水平的最佳区间。
