To improve the performance of mobile video delivery, caching layered videos at a site near to mobile end users (e.g., at the edge of mobile service provider's backbone) was advocated because cached videos can be delivered to mobile users with a high quality of experience, e.g., a short latency. How to optimally cache layered videos based on caching price, the available capacity of cache nodes, and the social features of mobile users, however, is still a challenging issue. In this paper, we propose a novel edge caching scheme to cache layered videos. First, a framework to cache layered videos is presented in which a cache node stores layered videos for multiple social groups, formed by mobile users based on their requests. Due to the limited capacity of the cache node, these social groups compete with each other for the number of layers they request to cache, aiming at maximizing their utilities while all mobile users in each group share the cost involved in the cache of video contents. Second, a Stackelberg game model is developed to study the interaction among multiple social groups and the cache node, and a noncooperative game model is introduced to analyze the competition among mobile users in different social groups. Third, leveraging the backward induction method, the optimal strategy of each player in the game model is proposed. Finally, simulation results show that the proposed method outperforms the exiting counterparts with a higher hit ratio and lower delay of delivering video contents.