Abstract
We consider a fair division model in which agents have general valuations for bundles of indivisible items. We propose two new approximate properties for envy freeness of allocations in this model: DEFX and DEF1. We compare these with two existing axiomatic properties: EFX and EF1. For example, we give the first result confirming that EFX allocations may not exist with general but identical valuations. However, even when they do exist in such problems, we prove that DEFX (and, therefore DEF1) and PO allocations exist whereas EFX and PO allocations may not exist. Our results assert eloquently that DEFX and DEF1 approximate fairness better than EFX and EF1.
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Acknowledgements
Martin Aleksandrov was supported by the DFG Individual Research Grant on “Fairness and Efficiency in Emerging Vehicle Routing Problems” (497791398).
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Aleksandrov, M. (2022). Envy Freeness Up to One Item: Shall We Duplicate or Remove Resources?. In: Marreiros, G., Martins, B., Paiva, A., Ribeiro, B., Sardinha, A. (eds) Progress in Artificial Intelligence. EPIA 2022. Lecture Notes in Computer Science(), vol 13566. Springer, Cham. https://doi.org/10.1007/978-3-031-16474-3_59
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