Social Internet of Things (SIoT) is a control paradigm by the integration of social networking concepts into the Internet of Things, and Fog Computing (FC) is an emerging technology that is aimed at moving the cloud computing facilities to the access network. Recently, the SIoT and FC models are combined by using complementary features, and a new Social Fog IoT (SFIoT) paradigm has been developed. In this paper, we design novel resource allocation algorithms for the SFIoT system. Considering the social relationship and each preference, mobile devices in the SFIoT effectively share the limited computation and communication resources of FC operators. To formulate the interaction among mobile devices and FC operator, we adopt the basic concept of two game models: voting and bargaining games. Bicooperative voting approach can make control decisions for the resource allocation method, and Nash bargaining solution is used to effectively distribute the computation resource to different application tasks. Based on the two-phase game model, the proposed scheme takes various benefits in a fair-efficient way. Through the extensive simulation experiments, we can validate the superiority of our proposed approach by the fact that it produces a mutually acceptable agreement among game players and significantly outperforms the existing protocols. Last, we point out the further challenges and future research issues about the SFIoT paradigm opportunities.