Coordination Games on Multiplex Networks: Consensus, Convergence, and Stability of Opinion Dynamics

TL;DR

This paper analyzes opinion dynamics in multilayer social networks, showing how layer interactions influence consensus formation, convergence speed, and stability, with implications for network design.

Contribution

It introduces models for multilayer opinion dynamics, derives conditions for consensus, and reveals how layer interactions can both promote and hinder consensus.

Findings

Multilayer interactions can induce or accelerate consensus.

Layer similarity influences the effectiveness of merging or switching.

Interconnected layers can destabilize previously stable consensus.

Abstract

This paper studies opinion dynamics in multilayer (social) networks. Extending a single-layer model, we formulate opinion updates as a synchronous coordination game in which agents minimize a local cost to stay close to their neighbors' opinions. We propose two coupling mechanisms between layers: (i) a merged model that aggregates layers through weighted influences, and (ii) a switching model that periodically alternates across layers. Using random-walk and spectral analysis, we derive sufficient conditions for consensus, characterize convergence rates, and analyze stability under network perturbations. We show that multilayer interactions can induce or accelerate global consensus even when no single layer achieves it alone, and conversely, that individually coordinated layers may lose consensus once interconnected. Notably, we show that similarity between the layers (as captured by alignments in the weighted degrees of the nodes) is a main determinant of if merging or switching can speed up convergence to consensus compared to when the layers operate in isolation, providing guidelines for network design interventions.