starpg50_fast_bc.m from The effect of network topology on optimal exploration strategies and the evolution of cooperation in a mobile population

We model a mobile population interacting over an underlying spatial structure using a Markov movement model. Interactions take the form of public goods games, and can feature an arbitrary group size. Individuals choose strategically to remain at their current location or to move to a neighbouring location, depending upon their exploration strategy and the current composition of their group. This builds upon previous work where the underlying structure was a complete graph (i.e. there was effectively no structure). Here, we consider alternative network structures and a wider variety of, mainly larger, populations. Previously, we had found when cooperation could evolve, depending upon the values of a range of population parameters. In our current work, we see that the complete graph considered before promotes stability, with populations of cooperators or defectors being relatively hard to replace. By contrast, the star graph promotes instability, and often neither type of population can resist replacement. We discuss potential reasons for this in terms of network topology.

本研究采用马尔可夫运动模型（Markov movement model），对依托底层空间结构开展交互的移动种群进行建模。种群间的交互以公共物品博弈（public goods game）为形式，且支持任意规模的群组。个体将结合自身的探索策略与当前群组的组成情况，策略性地选择停留在当前位置，或是迁移至邻近位置。本研究基于此前的研究工作拓展而来：此前的研究中，底层空间结构为完全图（complete graph），即实际上不存在结构化约束。本次研究则考虑多种替代网络结构，并针对更多样化（以大规模种群为主）的种群展开分析。此前的研究发现，合作行为能否演化，取决于一系列种群参数的取值。在本次研究中，我们发现此前采用的完全图结构能够提升种群稳定性，合作者或背叛者构成的种群相对难以被替换。与之形成对比的是，星型图（star graph）会加剧种群不稳定性，两类种群往往都难以抵御替换。本研究将从网络拓扑（network topology）的角度，探讨产生这一现象的潜在原因。