On Pareto-Efficiency Between Revenue and Utility in Resource Allocation

In the broadband mobile service market, it is reasonable that the carrier (service provider) should choose a Pareto-efficient resource allocation policy so that both the revenue of the carrier and the utility of users can be maximized. In this paper, we investigate the fundamental problem of the existence of resource allocation policies that are Pareto-efficient between the revenue and the utility. We show that the revenue-maximizing policy is not always equal to the utility-maximizing policy and that the two distinct policies, if any, generate a set of Pareto-efficient resource allocation policies. To make a Pareto-efficient resource allocation schedule, we develop a mathematical framework, where we study the existence of the Pareto-efficient policies, a necessary and sufficient condition for Pareto-efficiency, which can be used for finding the set of all the Pareto-efficient policies, and an efficient and exact solution method to find a Pareto-efficient resource allocation schedule.