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Exploiting Social Tie Structure for Cooperative Wireless Networking: A Social Group Utility Maximization Framework

In this paper, we develop a social group utility maximization (SGUM) framework for cooperative wireless networking that takes into account both social relationships and physical coupling among users. We show that this framework provides rich modeling flexibility and spans the continuum between non-cooperative game and network utility maximization (NUM) -- two traditionally disjoint paradigms for network optimization. Based on this framework, we study three important applications of SGUM, in database assisted spectrum access, power control, and random access control, respectively. For the case of database assisted spectrum access, we show that the SGUM game is a potential game and always admits a socially-aware Nash equilibrium (SNE). We develop a randomized distributed spectrum access algorithm that can asymptotically converge to the optimal SNE, derive upper bounds on the convergence time, and also quantify the trade-off between the performance and convergence time of the algorithm. We further show that the performance gap of SNE by the algorithm from the NUM solution decreases as the strength of social ties among users increases and the performance gap is zero when the strengths of social ties among users reach the maximum values. For the cases of power control and random access control, we show that there exists a unique SNE. Furthermore, as the strength of social ties increases from the minimum to the maximum, a player's SNE strategy migrates from the Nash equilibrium strategy in a standard non-cooperative game to the socially-optimal strategy in network utility maximization. Furthermore, we show that the SGUM framework can be generalized to take into account both positive and negative social ties among users and can be a useful tool for studying network security problems.