Nonrational Game-Theoretic Opinion Dynamics for Privacy-Preserving Distributed Consensus in Multiagent Systems

Abstract

This article addresses distributed consensus and collective intelligence in multiagent systems applied to social computing contexts, where agents must coordinate under privacy constraints and bounded rationality. We propose a computation framework integrating adaptive opinion dynamics, graph neural networks (GNNs), deep reinforcement learning (DRL), and federated learning (FL) within a nonrational game-theoretic foundation. The key contribution is an enhanced opinion dynamics model incorporating time-varying confidence bounds and asymmetric influence mechanisms, enabling exponential consensus beyond classical bounded confidence models. A privacy-preserving GNN-DRL-FL architecture achieves distributed coordination through spatial aggregation and decentralized parameter synchronization with $\epsilon$-differential privacy guarantees. The coupling between opinion consensus and behavioral coordination is proven stable via linear matrix inequality (LMI) optimization. Theoretical analysis confirms convergence to Nash equilibrium, despite incomplete information and cognitive limitations. Comprehensive simulations covering comparative, scalability, privacy-ablation, and robustness studies confirm consistent gains in collective reward, energy efficiency, conflict avoidance, and privacy resilience over competing baselines.