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.
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de Keijzer, B., Bouveret, S., Klos, T., Zhang, Y. (2009). On the Complexity of Efficiency and Envy-Freeness in Fair Division of Indivisible Goods with Additive Preferences. In: Rossi, F., Tsoukias, A. (eds) Algorithmic Decision Theory. ADT 2009. Lecture Notes in Computer Science(), vol 5783. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04428-1_9
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DOI: https://doi.org/10.1007/978-3-642-04428-1_9
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