Coevolutionary Dynamics of Actions and Opinions in Social Networks

TL;DR

This paper introduces a coevolutionary model linking opinion formation and decision-making in social networks, proving convergence to equilibria and analyzing polarization and pluralistic ignorance through simulations.

Contribution

It presents a novel coevolutionary framework combining actions and opinions on a two-layer network, with theoretical convergence results and analysis of polarization phenomena.

Findings

Actions converge in finite steps

Opinions converge asymptotically

Polarized equilibria can emerge under certain conditions

Abstract

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.