Coevolution of Actions and Opinions in Networks of Coordinating and Anti-Coordinating Agents

TL;DR

This paper models how agents with coordinating or anti-coordinating behaviors evolve their actions and opinions on networks, revealing conditions for convergence to equilibria and the influence of network structure.

Contribution

It introduces a coevolutionary model combining actions and opinions on two-layer networks, analyzing convergence and equilibrium conditions for both agent types.

Findings

Convergence to Nash equilibrium is guaranteed for coordinating agents.

All trajectories of anti-coordinating agents converge to a Nash equilibrium.

Analytical conditions for consensus and polarization depend on network structure.

Abstract

In this paper, we investigate the dynamics of coordinating and anti-coordinating agents in a coevolutionary model for actions and opinions. In the model, the individuals of a population interact on a two-layer network, sharing their opinions and observing others' action, while revising their own opinions and actions according to a game-theoretic mechanism, grounded in the social psychology literature. First, we consider the scenario of coordinating agents, where convergence to a Nash equilibrium (NE) is guaranteed. We identify conditions for reaching consensus configurations and establish regions of attraction for these equilibria. Second, we study networks of anti-coordinating agents. In this second scenario, we prove that all trajectories converge to a NE by leveraging potential game theory. Then, we establish analytical conditions on the network structure and model parameters to guarantee the existence of consensus and polarized equilibria, characterizing their regions of attraction.