Coevolutionary Dynamics of Actions and Opinions in Social Networks
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Modeling opinion formation and decision-making processes, important in their own rights, have been treated as separate problems in the study of dynamical models for social networks. Empirical studies suggest a deep intertwining between these two processes, and in this paper, we bridge the gap in the existing research by proposing a novel coevolutionary model. In the model, each individual can select an action from a binary set, and also holds an opinion on which action they prefer. Actions and opinions coevolve on a two-layer network structure. Under some reasonable assumptions on the network structure and asynchronous updating mechanics, we use rigorous analysis to establish that for all initial conditions, the actions converge in a finite number of time steps while opinions converge asymptotically. Next, we provide sufficient conditions for the emergence and the stability of polarized equilibria, whereby the population splits into two communities, each selecting and supporting one of the actions. Finally, numerical simulations are used to examine "pluralistic ignorance", whereby a social group incorrectly assumes the opinions of others due to the actions observed.
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