Wireless body area networks (WBANs) are cyber-physical systems that emerged as a key technology to provide real-time health monitoring and ubiquitous healthcare services. WBANs could operate in dense environments such as in a hospital and lead to a high mutual communication interference in many application scenarios. The excessive interferences will significantly degrade the network performance, including depleting the energy of WBAN nodes more quickly and even eventually jeopardize people's lives because of unreliable (caused by the interference) healthcare data collections. Therefore, it is critical to mitigate the interference among WBANs to increase the reliability of the WBAN system while minimizing the system power consumption. Many existing approaches can deal with communication interference mitigation in general wireless networks but are not suitable for WBANs because of ignoring the social nature of WBANs by them. Unlike the previous research, we for the first time propose a power game based approach to mitigate the communication interferences for WBANs based on the people's social interaction information. Our major contributions include: 1) modeling the inter-WBANs interference and determine the distance distribution of the interference through both theoretical analysis and Monte Carlo simulations; 2) developing social interaction detection and prediction algorithms for people carrying WBANs; and 3) developing a power control game based on the social interaction information to maximize the system's utility while minimize the energy consumption of WBANs system. The extensive simulation results show the effectiveness of the power control game for inter-WBAN interference mitigation using social interaction information. Our research opens a new research vista of WBANs using social networks.