Stackelberg Bayesian Game for Power Allocation in Two-Tier Networks

The downlink power allocation in a two-tier cellular network that consists of a macrocell network underlaid by multiple femtocell networks is addressed in this paper. This paper aims to maximize the transmission capacity of the femtocell networks while guaranteeing that the interference experienced at the macro base station does not exceed an interference constraint. We formulate a Bayesian Stackelberg game to model and analyze behaviors of macrocell and femtocell base stations (MBS and FBSs, respectively). In this game, the MBS is the leader, whereas the FBSs are the followers. The channel information between an FBS and its associated femtocell user is private information and is considered the type of the follower. The leader issues the price of interference charged to the followers first to maximize its own profit. Based on the price, the followers decide the strategies to maximize their payoffs defined as the difference between the transmission capacity and the cost of interference (CoI) paid to the leader. Using backward induction, we first analyze the follower game. The existence and uniqueness of the Bayesian Nash equilibrium (BNE) are examined, and the methods to obtain the BNE for a symmetric case are provided. Then, the leader game is analyzed. Finally, the numerical analysis is provided.