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We propose a two-layer, semi-decentralized algorithm to compute a local solution to the Stackelberg equilibrium problem in aggregative games with coupling constraints. Specifically, we focus on a single-leader, multiple-follower problem, and after equivalently recasting the Stackelberg game as a mathematical program with complementarity constraints (MPCC), we iteratively convexify a regularized version of the MPCC as inner problem, whose solution generates a sequence of feasible descent directions for the original MPCC. Thus, by pursuing a descent direction at every outer iteration, we establish convergence to a local Stackelberg equilibrium. Finally, the proposed algorithm is tested on a numerical case study, a hierarchical instance of the charging coordination problem of Plug-in Electric Vehicles (PEVs).

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In this paper, a novel approach for interference pricing and power control in the uplink of a two-tier small cell network is proposed. To model this problem, a Stackelberg game is formulated in which the macrocell base station (MBS) and the femtocell user equipments (FUEs) are the players that seek to maximize their utility. In this game, the MBS optimizes its revenue which depends on the interference quota sold to the FUEs while the FUEs optimize the utility that captures the tradeoff between rate and payment to the MBS. Here, the MBS (leader) must choose an optimal price in order to manage the interference level from the FUEs (followers). To solve this game, a two-step distributed interference price bargaining algorithm is proposed. Using a number of techniques, the convergence of the proposed algorithm to a Stackelberg equilibrium is shown analytically. Simulation results show that this approach converges for a wide range of channel power gains while maintaining a certain energy efficiency level for the transmitting users.

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