We provide a new mathematical framework for the classic problem of fair allocation of indivisible goods, showing that it can be formulated as the problem of finding an optimal column rearrangement of multi- ple matrices. Based on this formulation, we design two novel algorithms called MinCov and MinCovTar- get to find optimal allocations under the newly introduced notion of minimum social inequality, and the popular notion of minimum envy. Numerical illustrations show an excellent performance of the newly developed algorithms also with respect to other allocation criteria, in particular for the maximum Nash welfare.

Fair allocation of indivisible goods with minimum inequality or minimum envy / D. Cornilly, G. Puccetti, L. Rüschendorf, S. Vanduffel. - In: EUROPEAN JOURNAL OF OPERATIONAL RESEARCH. - ISSN 0377-2217. - 279:2(2022 Mar 01), pp. 741-752. [10.1016/j.ejor.2021.06.020]

Fair allocation of indivisible goods with minimum inequality or minimum envy

G. Puccetti
Secondo
;
2022-03-01

Abstract

We provide a new mathematical framework for the classic problem of fair allocation of indivisible goods, showing that it can be formulated as the problem of finding an optimal column rearrangement of multi- ple matrices. Based on this formulation, we design two novel algorithms called MinCov and MinCovTar- get to find optimal allocations under the newly introduced notion of minimum social inequality, and the popular notion of minimum envy. Numerical illustrations show an excellent performance of the newly developed algorithms also with respect to other allocation criteria, in particular for the maximum Nash welfare.
Decision analysis; Algorithms for fair allocation; Perfect social equality; Minimum envy; Maximum Nash welfare; Pareto optimality
Settore SECS-S/06 - Metodi mat. dell'economia e Scienze Attuariali e Finanziarie
Settore MAT/06 - Probabilita' e Statistica Matematica
29-giu-2021
https://doi.org/10.1016/j.ejor.2021.06.020
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2434/861717
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