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: (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. Numerical experiments validate the theory and highlight the impact of layer weights and switching periods. These results clarify how cross-network interactions shape coordination and information diffusion across interconnected systems.

翻译：本文研究多层社交网络中的意见动态。通过扩展单层模型，我们将意见更新表述为一种同步协调博弈，其中智能体通过最小化局部成本以保持与邻居意见的接近度。我们提出两种耦合机制：(i) 通过加权影响聚合各层的合并模型，以及 (ii) 在各层间周期性交替的切换模型。利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，即使没有任何单层网络能独立达成共识，多层交互仍可诱发或加速全局共识；反之，原本各自协调的网络层在相互连接后可能丧失共识。数值实验验证了理论结果，并揭示了层间权重与切换周期的影响。这些结论阐明了跨网络交互如何影响互联系统中的协调行为与信息传播。