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

2025-05-06

AI Summary

This paper investigates the coevolutionary dynamics of opinions and behaviors among coordinating and anticoordinating agents in bilayer networks. To model heterogeneous agent interactions, we propose a coevolutionary framework integrating potential games with social-psychological mechanisms, enabling simultaneous opinion updating and behavioral observation. Methodologically, we unify the convergence analysis for both agent types: we rigorously prove global convergence to consensus equilibria in coordinating networks under specific structural conditions and characterize their basins of attraction; we establish that anticoordinating networks necessarily converge to Nash equilibria, with polarization as the sole possible stable state; and we derive analytical necessary and sufficient conditions—governed jointly by network topology and strategy parameters—for the existence of consensus versus polarized equilibria. These results provide a theoretical framework and quantitative tools for understanding how heterogeneous social interactions drive collective behavior in complex systems.

Technology Category

• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Coordination and Collaboration
• Cognitive Modeling & Cognitive Systems: Social Cognition And Interaction

Application Category

• Social Networks and Social Media: Media and governance, opinion dynamics, filter bubbles, polarization
• Economics, Online Markets and Human Computation: Social networks and social learning
• Web Mining and Content Analysis: Models for Web evolution

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.

Problem

• Study dynamics of coordinating agents in coevolutionary networks
• Analyze anti-coordinating agents' convergence to Nash equilibrium
• Identify conditions for consensus and polarized equilibria

Innovation

• Two-layer network for opinion and action interaction
• Game-theoretic mechanism for opinion revision
• Potential game theory for NE convergence