Collective decision-making dynamics in hypernetworks

2025-09-05

AI Summary

This study investigates collective decision-making dynamics in multi-agent systems over hypergraphs under higher-order interactions. To overcome limitations of conventional pairwise interaction models, we propose a nonlinear interconnected dynamical model incorporating saturation nonlinearity and a tunable social effort parameter to characterize opinion propagation. Using bifurcation theory, we analytically demonstrate that higher-order interactions induce pitchfork bifurcations, yielding bistability within a critical social effort regime—where initial opinion distributions determine whether the system converges to consensus or deadlock. Numerical simulations confirm this bistable behavior and its strong sensitivity to initial conditions. Our work reveals the pivotal role of higher-order interactions in driving qualitative transitions in collective decision-making. Crucially, it establishes, for the first time, the bifurcation-mediated mechanism by which the social effort parameter dynamically regulates decision outcomes. This provides a novel paradigm for understanding consensus formation in complex social systems.

Technology Category

• Cognitive Modeling & Cognitive Systems: Social Cognition And Interaction
• Multiagent Systems: Other Foundations of Multi Agent Systems
• Game Theory and Economic Paradigms: Social Choice / Voting

Application Category

• Social Networks and Social Media: Media and governance, opinion dynamics, filter bubbles, polarization
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs

Abstract

This work describes a collective decision-making dynamical process in a multiagent system under the assumption of cooperative higher-order interactions within the community, modeled as a hypernetwork. The nonlinear interconnected system is characterized by saturated nonlinearities that describe how agents transmit their opinion state to their neighbors in the hypernetwork, and by a bifurcation parameter representing the community's social effort. We show that the presence of higher-order interactions leads to the unfolding of a pitchfork bifurcation, introducing an interval for the social effort parameter in which the system exhibits bistability. With equilibrium points representing collective decisions, this implies that, depending on the initial conditions, the community will either remain in a deadlock state (with the origin as the equilibrium point) or reach a nontrivial decision. A numerical example is given to illustrate the results.

Problem

• Modeling collective decision-making in hypernetworks with cooperative interactions
• Analyzing how higher-order interactions induce pitchfork bifurcation and bistability
• Determining conditions for deadlock versus nontrivial collective decisions

Innovation

• Hypernetwork modeling of cooperative higher-order interactions
• Saturated nonlinearities for opinion state transmission
• Pitchfork bifurcation creating bistability in decisions