Nakajima Yohei, Masuda Naoki
Department of Mathematical Informatics, The University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo , 113-8656, Japan.
J Math Biol. 2015 Feb;70(3):465-84. doi: 10.1007/s00285-014-0770-2. Epub 2014 Mar 8.
We investigate evolutionary dynamics of two-strategy matrix games with zealots in finite populations. Zealots are assumed to take either strategy regardless of the fitness. When the strategy selected by the zealots is the same, the fixation of the strategy selected by the zealots is a trivial outcome. We study fixation time in this scenario. We show that the fixation time is divided into three main regimes, in one of which the fixation time is short, and in the other two the fixation time is exponentially long in terms of the population size. Different from the case without zealots, there is a threshold selection intensity below which the fixation is fast for an arbitrary payoff matrix. We illustrate our results with examples of various social dilemma games.
我们研究了有限种群中存在狂热者的双策略矩阵博弈的进化动力学。假定狂热者无论适应度如何都采取某一策略。当狂热者选择的策略相同时，狂热者所选策略的固定是一个平凡结果。我们研究这种情况下的固定时间。我们表明固定时间分为三个主要阶段，其中一个阶段的固定时间较短，另外两个阶段的固定时间相对于种群大小呈指数增长。与没有狂热者的情况不同，存在一个阈值选择强度，低于该强度时，对于任意收益矩阵，固定都很快。我们用各种社会困境博弈的例子来说明我们的结果。
