On the Complexity of Efficiency and Envy-Freeness in Fair Division of Indivisible Goods with Additive Preferences

We study the problem of allocating a set of indivisible goods to a set of agents having additive preferences. We introduce two new important complexity results concerning efficiency and fairness in resource allocation problems: we prove that the problem of deciding whether a given allocation is Pareto-optimal is coNP-complete, and that the problem of deciding whether there is a Pareto-efficient and envy-free allocation is p 2 -complete.

• Type: Conference
• Year: 2009
• Where: ALDT
• Authors: Bart de Keijzer, Sylvain Bouveret, Tomas Klos, Yingqian Zhang
• Keywords: Additive Preferences, ALDT 2009, Algorithms, Resource Allocation Problems