Wireless Service Provider Selection and Bandwidth Resource Allocation in Multi-Tier HCNs

In this paper, we study the inter-linked problems of wireless service provider (WSP) selection of users and bandwidth allocation of WSPs in multi-tier heterogeneous cellular networks employing the approach combining stochastic geometry and game theory. In particular, the expected average user achievable rate is calculated by modeling the distributions of users and base stations (BSs) as independent homogeneous Poisson point processes. Moreover, a hierarchical game framework is presented to model the complicated interactions among users and WSPs. Wherein, the evolutionary game, non-cooperative game, and multi-leader multi-follower Stackelberg game models are, respectively, adopted to formulate the competition among users, competition among WSPs, and cyclic dependence between users and WSPs. According to backward induction, the formulated Stackelberg game would be solved after the formulated evolutionary game and non-cooperative game are sequentially studied. For the evolutionary game, both the closed-form expression and the asymptotically stability of its evolutionary equilibrium (EE) were analyzed. Then, conditioned on the obtained EE, the existence of Nash equilibrium (NE) for the non-cooperative bandwidth allocation game is established; furthermore, a sufficient condition for the uniqueness of the NE is derived. Finally, extensive simulation results verify both the validity of our analysis and the effectiveness of the proposed scheme.