Hierarchical Competition in Femtocell-Based Cellular Networks

This paper considers the downlink power allocation problem in a cellular network where a bi-level hierarchy exists. The network is comprised of the macrocells underlaid with femtocells. The objective of each station in the network is to maximize its capacity under power constraints. The problem is formulated as a Stackelberg game with the macrocell base stations as the leaders and the femtocell access points as the followers. The leaders are assumed to have enough information and foresight to consider the response of the followers while formulating their strategies. To characterize such interaction between leaders and followers, Stackelberg equilibrium is introduced; and it is shown to exist under the assumption of continuity of best response function of the leader sub-game. %For the case of Nash games, the relationship between the upper and lower sub-game equilibrium is explored.