Complexity and approximability of social welfare optimization in multiagent resource allocation

Abstract

An important task in multiagent resource allocation, which provides mechanisms to allocate bundles of (indivisible and nonshareable) resources to agents, is to maximize social welfare. We study the computational complexity of exact social welfare optimization by the Nash product, which can be seen as a sensible compromise between the well-known notions of utilitarian and egalitarian social welfare. When utilitiy functions are represented in the bundle or the k-additive form, for k ≥ 3, we prove that the corresponding computational problems are DP-complete (where DP denotes the second level of the boolean hierarchy over NP), thus confirming two conjectures raised by Roos and Rothe [10]. We also study the approximability of social welfare optimization problems.