Pareto efficiency of pricing-based power control in wireless data networks

Recent work has considered power control for wireless data networks from the framework of microeconomics. The user preferences have been mapped to utility functions measured in useful bits transmitted per unit of battery energy. We consider utility maximizing distributed power control in the presence of pricing and study the existence and efficiency of equilibria achieved. Specifically, we investigate the Pareto efficiency of a pricing policy that punishes asocial behavior in terms of the transmit power used by each user and hence the interference caused by it. The Nash equilibria achieved under pricing are characterized by using supermodularity. We propose a simple implementation of the pricing scheme where the base station broadcasts a pricing parameter that users use in their distributed power control algorithm. With the appropriate choice of the pricing parameter, all users increase their utilities significantly as compared to the case where there is no pricing. We also discuss the implication of pricing with regard to achieving a socially optimum operating point