Costly bilingualism model in a population with one zealot

TL;DR

This paper models costly bilingualism in populations with a zealot, analyzing how local interactions and network structure influence cascading adoption of strategies, revealing that local interactions and zealot placement significantly impact outcomes.

Contribution

It introduces a model of costly bilingualism with a zealot, examining the effects of interaction range and network heterogeneity on strategy cascades.

Findings

Local interactions hinder the adoption of superior strategies.

Zealot placement affects the size of cascades in networks.

Global interactions facilitate strategy spreading.

Abstract

We consider a costly bilingualism model in which one can take two strategies in parallel. We investigate how a single zealot triggers the cascading behavior and how the compatibility of the two strategies affects when interacting patterns change. First, the role of the interaction range on the cascading is studied by increasing the range from local to global. We find that people sometimes do not favor to take the superior strategy even though its payoff is higher than that of the inferior one. This is found to be caused by the local interactions rather than the global ones. Applying this model to social networks, we find that the location of the zealot is also important for larger cascading in heterogeneous networks.