Abstract
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.
Highlights
A standard assumption underlying evolutionary game dynamics, regardless of whether a player is social agent or gene, is that players tend to imitate successful others
Because the mean fixation time is by definition the largest for i = 0, i.e., the initial condition in which all ordinary players select B, we focus on t0
The mea√n fixation time in the limit of large N is given by t0 ∝ N ln N in case (i) and t0 ∝ N exp(γ N ) (γ > 0) in cases (ii) and (iii)
Summary
A standard assumption underlying evolutionary game dynamics, regardless of whether a player is social agent or gene, is that players tend to imitate successful others. Collective social dynamics in the presence of zealots started to be examined for non-game situations such as the voter model representing competition between two strong opinions (i.e., neutral invasions) (Mobilia 2003; Galam and Jacobs 2007; Mobilia et al 2007; Xie et al 2011; Singh et al 2012). Voluntary immunization behavior of individuals when epidemic spreading possibly occurs in a population can be examined by a public-goods dilemma game (Fu et al 2011).
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