Multi-Topic Projected Opinion Dynamics for Resource Allocation

2025-09-09

AI Summary

This paper investigates the opinion dynamics of multiple agents engaged in multi-issue resource allocation under budget constraints and social network influence. We propose a projected dynamical system model that jointly incorporates issue-specific preferences, resource constraints, and social influence. We rigorously prove that all trajectories converge to a nonempty equilibrium set. Furthermore, we establish that the system is fundamentally a potential game, thereby forging a theoretical correspondence between opinion dynamics equilibria and Nash equilibria; under acyclic (i.e., antagonism-free) network topologies, we derive a sufficient condition for equilibrium uniqueness. Leveraging tools from potential game theory, graph theory, and constrained optimization, we validate—through both theoretical analysis and numerical simulations—the model’s convergence properties, equilibrium uniqueness guarantees, and empirical interpretability in real-world resource allocation scenarios.

Technology Category

• Game Theory and Economic Paradigms: Equilibrium
• Multiagent Systems: Mechanism Design
• Knowledge Representation and Reasoning: Preferences

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: Efficient manipulation of static and dynamic Web-related graphs

Abstract

We propose a model of opinion formation on resource allocation among multiple topics by multiple agents, who are subject to hard budget constraints. We define a utility function for each agent and then derive a projected dynamical system model of opinion evolution assuming that each agent myopically seeks to maximize its utility subject to its constraints. Inter-agent coupling arises from an undirected social network, while inter-topic coupling arises from resource constraints. We show that opinions always converge to the equilibrium set. For special networks with very weak antagonistic relations, the opinions converge to a unique equilibrium point. We further show that the underlying opinion formation game is a potential game. We relate the equilibria of the dynamics and the Nash equilibria of the game and characterize the unique Nash equilibrium for networks with no antagonistic relations. Finally, simulations illustrate our findings.

Problem

• Modeling opinion formation on multi-topic resource allocation
• Analyzing opinion convergence under budget and network constraints
• Characterizing equilibrium states in opinion formation games

Innovation

• Projected dynamical system for opinion evolution
• Utility maximization under budget constraints
• Potential game framework for equilibrium analysis