—In this work, the inter-linked problems of wireless service provider (WSP) selection by users and bandwidth allocation by WSPs in multi-tier heterogeneous cellular networks (HCNs) are addressed. This paper employs the approach combining stochastic geometry and game theory to solve these problems. Particularly, the expected average achievable rate for each user is calculated by modeling the distributions of users and base stations (BSs) as independent homogeneous Poisson Point Process (PPP) and a hierarchical game framework is presented to investigate the interactions between users and WSPs. In this framework, the evolutionary game, non-cooperative game and multi-leader multi-follower Stackelberg game models are adopted to formulate the competition among users, competition among WSPs and interaction among users and WSPs, respectively. Moreover, for the formulated evolutionary game, the evolutionary equilibrium (EE) was investigated and its asymptotically stability was analyzed after deriving its closed form expression. Then, conditioned on the obtained EE, a non-cooperative spectrum bandwidth allocation game (N-BAG) has been formulated to investigate the bandwidth allocation of WSPs. The existence of Nash equilibrium (NE) for N-BAG has been proven and an offline algorithm to achieve the equilibrium state was proposed. Finally, simulation results verify the validity of the analysis and demonstrate that a unique NE would be achieved by the HCNs adopting the proposed scheme.
['Chao Xu', 'Min Sheng', 'Vineeth S. Varma', 'Tony Q. S. Quek', 'Jiandong Li']
Wireless service provider selection and bandwidth resource allocation in multi-tier HCNs