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

Abstract

Social utility maximization refers to the process of allocating resources in such a way that the sum of agents' utilities is maximized 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 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. The construction of the mechanism is done in a systematic way by considering the dual optimization problem. In addition to the required properties of efficiency and individual rationality that such mechanisms ought to satisfy, three 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, and c) strong budget balance at equilibrium and also off equilibrium whenever demand is feasible.