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

@inproceedings{Keijzer2009OnTC,
  title={On the Complexity of Efficiency and Envy-Freeness in Fair Division of Indivisible Goods with Additive Preferences},
  author={Bart de Keijzer and Sylvain Bouveret and Tomas Klos and Yingqian Zhang},
  booktitle={Algorithmic Decision Theory},
  year={2009}
}
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. 

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