Optimal linear pricing in power control game

The framework of power control based on economic concepts of utility and pricing has been proposed recently in wireless data systems. In this paper we present the non-cooperative power control game with pricing, and investigate the optimal linear pricing with both heterogeneous and homogeneous factors. On this basis we propose hierarchical iterative algorithms, in which individual users game with pricing without cooperation while the base station adjusts the linear factor of each user. These algorithms can move utilities at Nash equilibrium to the Pareto-optimal frontier, and their convergence properties are studied both theoretically and numerically. In the numerical simulation, a two-person game with the utility function based on throughput is illustrated.