circpg50.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.

我们采用马尔可夫运动模型（Markov movement model），对基于底层空间结构开展互动的移动种群进行建模。种群间的互动以公共品博弈（public goods game）为形式，且支持任意规模的群体。个体将基于自身的探索策略与当前群体的组成结构，策略性地选择停留在当前位置，或是迁移至邻近位置。本研究基于此前的相关工作展开——彼时的底层结构为完全图（complete graph），即本质上不存在空间结构；而在本研究中，我们考虑了多种替代网络结构，并针对规模更大、类型更丰富的种群展开分析。此前的研究已发现，合作行为能否演化，取决于一系列种群参数的取值。在本研究中，我们发现此前采用的完全图结构可提升种群稳定性，合作型种群与背叛型种群均较难被替代；与之形成对比的是，星型图结构则会加剧种群不稳定性，两类种群通常均难以抵御替代。我们将从网络拓扑（network topology）的角度，对上述现象的潜在成因展开讨论。