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

Abstract

This paper studies opinion dynamics in multilayer 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. A common thread arising from our analysis is that the alignment in the weighted degrees of the nodes between the two layers is the main determinant of whether merging or switching can speed up convergence to consensus compared to layers operating in isolation, providing network design intervention guidelines.