Cost-Effective Hybrid Control Strategies for Dynamical Propaganda War Game

Cyber propaganda wars significantly impact users on Online Social Networks (OSNs), potentially altering their psychological/ideological attitudes and behaviors. Understanding these behavioral dynamics necessitates models that can effectively capture the propagation of dual competitive information, encompassing both propaganda and counter-propaganda campaigns by both conflicting parties. However, current models do not adequately account for competitive information spreading in dual setting and it lacks efficient strategies for managing both propaganda and counter-propaganda investments. To bridge these gaps, our study presents an innovative netwORked dIfferENTial gAme wiTh hybrId cONtrol (ORIENTATION) framework that integrates differential game with 1) a degree-based network model characterizing the spreading dynamics of dual competitive information for both parties; and 2) a dual hybrid control mechanism consisting of investment rates by continuous-time propaganda and discrete-time counter-propaganda. Using this framework, we formulate the Hybrid-contrOlled Differential GamE (HODGE) problem. We theoretically derive the necessary conditions for Nash equilibrium, and develop an iterative algorithm, termed the HODGE algorithm, to numerically approximate the Nash equilibrium. Our experiments, performed on different groups of OSNs, reveal that the resulting strategy profiles consistently outperform several alternative profiles in terms of cost-effectiveness. Scalability assessment for the HODGE algorithm is then carried out on OSNs with different scales, demonstrating its strong performance in terms of computational efficiency, scalability and practicability. Additional experimental results suggest that a decrease in the lower bounds of the investment rates in both propaganda and counter-propaganda campaigns and an early implementation of counter-propaganda strategies can significantly enhance cost-effectiveness, offering strategic insights for those engaged in cyber propaganda war.