On Fair Division under Heterogeneous Matroid Constraints

Amitay Dror, Michal Feldman, Erel Segal-Halevi

Research output: Contribution to journalArticlepeer-review

Abstract

We study fair allocation of indivisible goods among additive agents with feasibility constraints. In these settings, every agent is restricted to get a bundle among a specified set of feasible bundles. Such scenarios have been of great interest to the AI community due to their applicability to real-world problems. Following some impossibility results, we restrict attention to matroid feasibility constraints that capture natural scenarios, such as the allocation of shifts to medical doctors and the allocation of conference papers to referees. We focus on the common fairness notion of envy-freeness up to one good (EF1). Previous algorithms for finding EF1 allocations are either restricted to agents with identical feasibility constraints or allow free disposal of items. An open problem is the existence of EF1 complete allocations among agents who differ both in their valuations and in their feasibility constraints. In this work, we make progress on this problem by providing positive and negative results for several matroid and valuation types. Among other results, we devise polynomial-time algorithms for finding EF1 allocations in the following settings: (i) n agents with heterogeneous (non-identical) binary valuations and partition matroids with heterogeneous capacities; (ii) two agents with heterogeneous additive valuations and partition matroids with heterogeneous capacities; and (iii) three agents with heterogeneous binary valuations and identical base-orderable matroid constraints.

Original languageEnglish
Pages (from-to)567-611
Number of pages45
JournalJournal of Artificial Intelligence Research
Volume76
DOIs
StatePublished - 2023

Funding

FundersFunder number
Horizon 2020 Framework Programme866132
European Research Council
Israel Science Foundation712/20, 317/17

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