Empirical studies suggest a deep intertwining between opinion formation and decision-making processes, but these have been treated as separate problems in the study of dynamical models for social networks. In this paper, we bridge the gap in the literature by proposing a novel coevolutionary model, in which each individual selects an action from a binary set and has an opinion on which action they prefer. Actions and opinions coevolve on a two-layer network. For homogeneous parameters, undirected networks, and under reasonable assumptions on the asynchronous updating mechanics, we prove that the coevolutionary dynamics is an ordinal potential game, enabling analysis via potential game theory. Specifically, we establish global convergence to the Nash equilibria of the game, proving that actions converge in a finite number of time steps, while opinions converge asymptotically. Next, we provide sufficient conditions for the existence of, and convergence to, polarized equilibria, whereby the population splits into two communities, each selecting and supporting one of the actions. Finally, we use simulations to examine the social psychological phenomenon of pluralistic ignorance.

翻译：实证研究表明，意见形成与决策过程之间存在深刻的相互交织，但在社交网络动力学模型的研究中，这两者一直被视为独立的问题。本文通过提出一种新颖的协同演化模型来填补文献中的这一空白，在该模型中，每个个体从二元集合中选择一个行动，并对其偏好的行动持有意见。行动与意见在双层网络上共同演化。对于同质参数、无向网络以及在异步更新机制的合理假设下，我们证明了该协同演化动力学是一个序数势博弈，从而能够借助势博弈论进行分析。具体而言，我们建立了向博弈纳什均衡的全局收敛性，证明行动在有限时间步内收敛，而意见则渐近收敛。接下来，我们提供了极化均衡存在及收敛的充分条件，在这种均衡下，群体分裂为两个社区，每个社区分别选择并支持其中一种行动。最后，我们利用仿真模拟研究了"多元无知"这一社会心理学现象。