A tale of two emergent games: opinion dynamics in dynamical directed networks

TL;DR

This paper models opinion dynamics in evolving directed social networks, revealing how unidirectional interactions influence network structure and opinion spread through emergent game-theoretic mechanisms.

Contribution

It introduces a voter model on dynamical directed networks and uncovers two distinct emergent games governing network degree and opinion fate.

Findings

Degree distribution is analytically derived for the evolving network.

Two different emergent games influence network structure and opinion dynamics.

Criteria are provided for minority opinion takeover based on in-group bias.

Abstract

Uni-directional social interactions are ubiquitous in real social networks whereas undirected interactions are intensively studied. We establish a voter model in a dynamical directed network. We analytically obtain the degree distribution of the evolving network at any given time. Furthermore, we find that the average degree is captured by an emergent game. On the other hand, we find that the fate of opinions is captured by another emergent game. Beyond expectation, the two emergent games are typically different due to the unidirectionality of the evolving networks. The Nash equilibrium analysis of the two games facilitates us to give the criterion under which the minority opinion with few disciples initially takes over the population eventually for in-group bias. Our work fosters the understanding of opinion dynamics ranging from methodology to research content.