A General Mechanism Design Methodology for Social Utility Maximization with Linear Constraints

Abstract

Social utility maximization refers to the process of allocating resources in a way that maximizes the sum of agents' utilities, under the system constraints. Such allocation arises in several problems in the general area of communications, including unicast (and multicast multi-rate) service on the Internet, as well as in applications with (local) public goods, such as power allocation in wireless networks, spectrum allocation, etc. Mechanisms that implement such allocations in Nash equilibrium have also been studied but either they do not possess the full implementation property, or are given in a case-by-case fashion, thus obscuring fundamental understanding of these problems. In this paper we propose a unified methodology for creating mechanisms that fully implement, in Nash equilibria, social utility maximizing functions arising in various contexts where the constraints are convex. Two additional design goals are the focus of this paper: a) the size of the message space scaling linearly with the number of agents (even if agents' types are entire valuation functions), b) allocation being feasible on and off equilibrium.