With the ubiquity of social networks, rumors spread easily, leading to increasing attention on their dissemination. In this context, the spread of rumors is influenced not only by the content of the information itself but also by the behavior of various actors over social networks. To model such a process, we propose a novel rumor propagation interaction model. This model, for the first time, combines a rumor-spreading model, characterizing the dual impact of media activities on rumor propagation, with a three-party evolutionary game model, exploring the interactions among netizens, media, and the government on social media platforms. To validate the model, we employ a physics-informed neural network to simulate real rumor-spread data from the U.S. Twitter platform. By integrating the estimated parameter set from the rumor-spreading model with the three-party evolutionary game model, we design a new tripartite evolutionary game matrix. This matrix effectively quantifies the government’s regulatory efforts, the media’s tendency to spread rumors, and the likelihood of netizens participating in rumor diffusion. The experimental results demonstrate that a higher probability of strict government control more effectively curbs the momentum of rumor spread, while a lower probability of media spreading rumors corresponds to an increase in the number of rumor debunkers. Reduced control costs lead to increased government intervention, less media-driven rumor propagation, and more frequent media refutations. In summary, this model demonstrates significant practical value for understanding rumor propagation dynamics.