Envy-freeness up to one item: Shall we add or remove resources?

06/19/2020

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by   Martin Aleksandrov, et al.

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We consider a fair division model in which agents have general valuations for bundles of indivisible items. We propose two new axiomatic properties for allocations in this model: EF1+- and EFX+-. We compare these with the existing EF1 and EFX. Although EF1 and EF1+- allocations often exist, our results assert eloquently that EFX+- and PO allocations exist in each case where EFX and PO allocations do not exist. Additionally, we prove several new impossibility and incompatibility results.