Optimal Subsidies for Shared Small Cell Networks —A Social Network Perspective

In this paper, we study the optimal differentiated subsidies from a mobile network operator (MNO) to form a shared small cell network using social network information. It is a win-win strategy for the MNO to offload data and for small cell users (SUs) to receive enhanced QoS. We formulate the problem as a Stackelberg Game: in Stage I, the MNO sets differentiated subsidies and maximizes a subsidy elasticity of sharing metric, which captures the goal of using the least subsidies to obtain the most shared network; in Stage II, each SU decides the degree of sharing by maximizing a utility function, which is a tradeoff between proportional-fair capacity and subsidy. In our model, at subgame perfect equilibrium, the shared network can be maintained with the termination of subsidies. Our results can be summarized as follows. Firstly, we propose a deterministic framework where each SU´s type information is known to the MNO and show that SUs´ sharing strategies only depend on their type information. The subsidies act as intermediate variables, which will not affect the intrinsic structure of the shared network. The sensitivity analyses and the robust counterpart are investigated in terms of capacity perturbations and mobility uncertainties, respectively. Furthermore, we propose a dynamic framework by assuming that the mobility of each SU is an independent lazy random walk. We show that our proposed framework converges to the optimal solution at a geometric rate. Utilizing SU´s type information, our work provides a framework on how to formulate a stable shared network with a unique equilibrium via subsidies as intermediate helpers.