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

  • Authors:
  • Bart Keijzer;Sylvain Bouveret;Tomas Klos;Yingqian Zhang

  • Affiliations:
  • Delft University of Technology,;Onera-DTIM, Toulouse;Delft University of Technology,;Delft University of Technology,

  • Venue:
  • ADT '09 Proceedings of the 1st International Conference on Algorithmic Decision Theory
  • Year:
  • 2009

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Abstract

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 $\Sigma_2^p$-complete.