Critical mass effect in evolutionary games triggered by zealots

Alessio Cardillo,Naoki Masuda

doi:10.1103/physrevresearch.2.023305

Abstract

Tiny perturbations may trigger large responses in systems near criticality, shifting them across equilibria. Committed minorities are suggested to be responsible for the emergence of collective behaviors in many physical, social, and biological systems. Using evolutionary game theory, we address the question whether a finite fraction of zealots can drive the system to large-scale coordination. We find that a tipping point exists in coordination games, whereas the same phenomenon depends on the selection pressure, update rule, and network structure in other types of games. Our study paves the way to understand social systems driven by the individuals' benefit in presence of zealots, such as human vaccination behavior or cooperative transports in animal groups.

Highlights

One hallmark of complex systems at the critical point is that small perturbations may trigger large responses, shifting the system from one equilibrium to another [1,2,3,4,5,6]
The lack of a critical mass effect observed in the Hawk and Dove (HD) and Prisoner’s dilemma (PD) games suggests the inability of zealots to initiate a positive feedback mechanism enabling large-scale invasion of cooperators
We have considered three evolutionary dilemmas, and observed that only the Stag hunt (SH) game displays a clear critical mass effect, whereas in the other two dilemmas we need to reduce the selection pressure, change the update rule, or consider heterogeneous networks to observe a critical mass effect

Summary

Introduction

One hallmark of complex systems at the critical point is that small perturbations may trigger large responses, shifting the system from one equilibrium to another [1,2,3,4,5,6]. Zealotry can elicit consensus in human/animal behavior [18,19,20], the polarization of opinions in the voter model [21], majority rule [13], naming game [22,23,24], social knowledge structure (SKS) [25], and cooperative decision making model (CDMM) [26] models. An infinitesimal fraction of zealots is enough to shift the equilibria in the voter [21], CDMM [26], and Schelling’s [30] dynamics, whereas finite fractions are needed in both the majority rule [13] and Vicsek [9] dynamics, as well as in the naming game theoretically [22,24] and experimentally [32]

Objectives

Methods

Results

Conclusion