  This paper investigates the energy-efficient power allocation for a two-tier,
underlaid femtocell network. The behaviors of the Macrocell Base Station (MBS)
and the Femtocell Users (FUs) are modeled hierarchically as a Stackelberg game.
The MBS guarantees its own QoS requirement by charging the FUs individually
according to the cross-tier interference, and the FUs responds by controlling
the local transmit power non-cooperatively. Due to the limit of information
exchange in intra- and inter-tiers, a self-learning based strategy-updating
mechanism is proposed for each user to learn the equilibrium strategies. In the
same Stackelberg-game framework, two different scenarios based on the
continuous and discrete power profiles for the FUs are studied, respectively.
The self-learning schemes in the two scenarios are designed based on the local
best response. By studying the properties of the proposed game in the two
situations, the convergence property of the learning schemes is provided. The
simulation results are provided to support the theoretical finding in different
situations of the proposed game, and the efficiency of the learning schemes is
validated.
