Evolutionary dynamics in finite populations with zealots

TL;DR

This paper analyzes how the presence of zealots, who always choose a specific strategy, affects the fixation time in finite populations playing two-strategy games, revealing regimes of rapid and slow fixation.

Contribution

It introduces a detailed analysis of fixation times in finite populations with zealots, highlighting a threshold selection intensity and different fixation regimes.

Findings

Fixation time divided into three regimes: short and two exponentially long.

Existence of a threshold selection intensity for fast fixation.

Application to various social dilemma games.

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.