Cressman R, Vickers G T
Department of Mathematics, Wilfrid Laurier University, Waterloo, Ontario, Canada.
J Theor Biol. 1997 Feb 21;184(4):359-69. doi: 10.1006/jtbi.1996.0251.
Two models are considered for the study of game dynamics in a spatial domain. Both models are continuous in space and time and give rise to reaction-diffusion equations. The spatial domain is homogeneous but the mobility of the individuals is allowed to depend upon the strategy. The models are analysed for spatial patterns (via a Turing instability) and also for the direction of the travelling wave that replaces one strategy by another. It is shown that the qualitative behaviour of the two models is quite different. When considering the existence of spatial patterns and deciding whether increased mobility is helpful or not, it is shown that the answers depend crucially upon the model equations. Since both models (in the absence of spatial variation) are quite standard, it is clear that considerable care has to be exercised in the formulation of spatial models and in their interpretation.
为研究空间域中的博弈动力学，考虑了两种模型。这两种模型在空间和时间上都是连续的，并产生反应扩散方程。空间域是均匀的，但个体的迁移率允许取决于策略。对模型进行了空间模式分析（通过图灵不稳定性），并分析了一种策略被另一种策略取代的行波方向。结果表明，这两种模型的定性行为有很大不同。在考虑空间模式的存在以及确定迁移率增加是否有帮助时，结果表明答案关键取决于模型方程。由于两种模型（在没有空间变化的情况下）都是相当标准的，显然在空间模型的制定及其解释中必须格外小心。
