Social network services can not only help people form relationships and make new friends and partners, but also assist in processing personal information, sharing knowledge, and managing social relationships. Social networks achieve valuable communication and collaboration, bring additional business opportunities, and have great social value. Research on social network problems is effective by using assumption, definition, analysis, modeling, and optimization strategies. In this paper, we survey the existing problems of game theory applied to social networks and classify their application scenarios into four categories: information diffusion, behavior analysis, community detection, and information security. Readers can clearly master knowledge application in every category. Finally, we discuss certain limitations of game theory on the basis of research in recent years and propose future directions of social network research.