Complex Network Modeling With Power-Law Activating Patterns and Its Evolutionary Dynamics

2025-02-13

IEEE Transactions on Systems, Man, and Cybernetics: Systems

AI Summary

This study investigates how stochastic state switching (activation/silence) of individuals under power-law activation influences evolutionary game dynamics on complex networks, specifically focusing on the critical condition for cooperation emergence in the Prisoner’s Dilemma on homogeneous networks without mutation. Method: We propose the first network state-switching model incorporating power-law activation, rigorously establishing—via Markov chain analysis and renewal theory—the existence of a homogeneous stationary distribution and proving that activation size follows a power-law distribution. Leveraging statistical physics and evolutionary game theory, we derive an analytical criterion for cooperation emergence and quantify strategy absorptivity. The framework is further validated on empirical network topologies. Contribution/Results: Our key innovation lies in revealing how power-law activation reshapes the stationary distribution and lowers the threshold for cooperation, offering a novel paradigm for understanding collective behavior under intermittent interactions.

Technology Category

• Game Theory and Economic Paradigms: Cooperative Game Theory
• Multiagent Systems: Agent-Based Simulation and Emergent Behavior
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Social Networks and Social Media: Applications and emergent phenomena
• Web Mining and Content Analysis: Models for Web evolution
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

Complex network theory provides a unifying framework for the study of structured dynamic systems. The current literature emphasizes a widely reported phenomenon of intermittent interaction among network vertices. In this paper, we introduce a complex network model that considers the stochastic switching of individuals between activated and quiescent states at power-law rates and the corresponding evolutionary dynamics. By using the Markov chain and renewal theory, we discover a homogeneous stationary distribution of activated sizes in the network with power-law activating patterns and infer some statistical characteristics. To better understand the effect of power-law activating patterns, we study the two-person-two-strategy evolutionary game dynamics, demonstrate the absorbability of strategies, and obtain the critical cooperation conditions for prisoner's dilemmas in homogeneous networks without mutation. The evolutionary dynamics in real networks are also discussed. Our results provide a new perspective to analyze and understand social physics in time-evolving network systems.

Problem

• Model stochastic switching in complex networks
• Study power-law evolutionary game dynamics
• Analyze cooperation in prisoner's dilemmas

Innovation

• Power-law activating patterns
• Markov chain analysis
• Evolutionary game dynamics