Pacheco Jorge M, Traulsen Arne, Ohtsuki Hisashi, Nowak Martin A
ATP-Group and CFTC, Departamento de Física da Faculdade de Ciências, P-1649-003 Lisboa Codex, Portugal.
J Theor Biol. 2008 Feb 21;250(4):723-31. doi: 10.1016/j.jtbi.2007.10.040. Epub 2007 Nov 6.
Direct reciprocity relies on repeated encounters between the same two individuals. Here we examine the evolution of cooperation under direct reciprocity in dynamically structured populations. Individuals occupy the vertices of a graph, undergoing repeated interactions with their partners via the edges of the graph. Unlike the traditional approach to evolutionary game theory, where individuals meet at random and have no control over the frequency or duration of interactions, we consider a model in which individuals differ in the rate at which they seek new interactions. Moreover, once a link between two individuals has formed, the productivity of this link is evaluated. Links can be broken off at different rates. Whenever the active dynamics of links is sufficiently fast, population structure leads to a simple transformation of the payoff matrix, effectively changing the game under consideration, and hence paving the way for reciprocators to dominate defectors. We derive analytical conditions for evolutionary stability.
直接互惠依赖于同一两个个体之间的重复相遇。在此，我们研究动态结构化种群中直接互惠下合作的进化。个体占据图的顶点，通过图的边与他们的伙伴进行重复互动。与传统的进化博弈论方法不同，在传统方法中个体随机相遇且无法控制互动的频率或持续时间，我们考虑一个模型，其中个体在寻求新互动的速率上存在差异。此外，一旦两个个体之间形成了联系，就会评估这种联系的生产力。联系可以以不同速率中断。每当联系的活跃动态足够快时，种群结构会导致收益矩阵的简单变换，有效地改变所考虑的博弈，从而为互惠者主导背叛者铺平道路。我们推导出进化稳定性的分析条件。
