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This paper investigates rumor transmission over online social networks, such as those via Facebook or Twitter, where users liberally generate visible content to their followers, and the attractiveness of rumors varies over time and gives rise to opposition such as counter-rumors. All users in social media platforms are modeled as nodes in one of five compartments of a directed random graph: susceptible, hesitating, infected, mitigated, and recovered (SHIMR). The system is expressed with edge-based formulation and the transition dynamics are derived as a system of ordinary differential equations. We further allow individuals to decide whether to share, or disregard, or debunk the rumor so as to balance the potential gain and loss. This decision process is formulated as a game, and the condition to achieve mixed Nash equilibrium is derived. The system dynamics under equilibrium are solved and verified based on simulation results. A series of parametric analyses are conducted to investigate the factors that affect the transmission process. Insights are drawn from these results to help social media platforms design proper control strategies that can enhance the robustness of the online community against rumors.

Rumor Transmission in Online Social Networks Under Nash Equilibrium of a Psychological Decision Game