  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.
