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.

中文翻译：

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用于动态宣传战争游戏的经济高效的混合控制策略


网络宣传战对在线社交网络 （OSN） 上的用户产生了重大影响，可能会改变他们的心理/意识形态态度和行为。理解这些行为动态需要能够有效捕捉双重竞争信息传播的模型，包括冲突双方的宣传和反宣传活动。然而，目前的模型没有充分考虑双重环境中的竞争性信息传播，并且缺乏管理宣传和反宣传投资的有效策略。为了弥合这些差距，我们的研究提出了一个创新的 netwORked dIfferENTial gAme wiTh hybrId cONtrol （ORIENTATION） 框架，该框架将差分博弈与 1） 一个基于度的网络模型相结合，该模型描述了双方双重竞争信息的传播动态;2） 由连续时间宣传和离散时间反宣传的投资利率组成的双重混合控制机制。利用这个框架，我们制定了 Hybrid-contrOlled Differential GamE （HODGE） 问题。我们从理论上推导出纳什均衡的必要条件，并开发了一种迭代算法，称为 HODGE 算法，以数值近似纳什均衡。我们对不同组 OSN 进行的实验表明，在成本效益方面，生成的策略配置文件始终优于几种替代配置文件。然后，在不同尺度的 OSN 上对 HODGE 算法进行可扩展性评估，展示了其在计算效率、可扩展性和实用性方面的强大性能。 其他实验结果表明，降低宣传和反宣传活动投资率的下限以及尽早实施反宣传策略可以显著提高成本效益，为参与网络宣传战的人提供战略见解。