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.

翻译：本文研究多层网络中的意见动态问题。通过扩展单层模型，我们将意见更新过程建模为同步协调博弈，其中智能体通过最小化局部代价函数来保持与邻居意见的趋同。我们提出两种层间耦合机制：（i）融合模型，通过加权影响力聚合各层信息；（ii）切换模型，在各层之间周期性交替。运用随机游走与谱分析方法，我们推导出达成共识的充分条件，刻画收敛速率，并分析网络扰动下的稳定性。研究表明：即使单一层级无法独立促成共识，多层交互仍可诱发或加速全局共识；反之，原本各自协调的层级在互联后可能失去共识。分析揭示的核心规律是：两层节点加权度的一致性，是判断融合或切换机制能否比独立分层运行更快达成共识的主要决定因素，这为网络设计干预提供了指导准则。