Social group utility maximization in mobile networks: From altruistic to malicious behavior

We develop a social group utility maximization (SGUM) game framework that takes into account both social relationships and physical coupling among users in a mobile network. Under the SGUM framework, each user aims to maximize its social group utility, defined as the weighted sum of the individual utilities of the users that have social ties with it. One distinctive merit of the SGUM framework is that it can capture complex social structure among mobile users, consisting of diverse “positive” and “negative” social ties, and hence it offers a platform spanning the rich continuum from zero-sum game (ZSG) to standard non-cooperative game (NCG) to network utility maximization (NUM) - traditionally disjoint paradigms for network management. We then study the SGUM-based game for two applications. For the SGUM-based random access control game, we show that there exists a unique social-aware Nash equilibrium (SNE). As the strength of social ties increases, each user´s access probability at the SNE migrates from its strategy for a ZSG to that for a standard NCG, and eventually to its social optimal strategy for NUM, while the social welfare of all users at the SNE improves gradually. We then turn our attention to the SGUM-based multi-channel cooperative jamming game, which is always a ZSG, and show that there exists a unique mixed strategy SNE. When the social tie strength between the legitimate user and the cooperative jammer exceeds certain threshold, the cooperative jammer always jams the eavesdropper on some channel at the SNE, which improves the social welfare of the legitimate user and cooperative jammer. Our results shed light on the impact of social ties on users´ strategies and social welfare. We believe that the SGUM framework will open a new door for exploring the social aspect of mobile networking.