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Preprint Sep 2026

Envy-Free Allocation of Indivisible Goods under Leontief Preferences

Envy-freeness is a fundamental notion of fairness in the allocation of indivisible goods. In this paper, we study envy-free allocation under Leontief preferences, which model perfect complements. Although Leontief preferences have been extensively studied in the context of allocating divisible goods and market equilibr...

Tanmay Inamdar, P. Jain, Pranjal Pandey · 0 citations
Preprint Sep 2026

Reconfiguration in Fair Division Revisited

We revisit reconfiguration in the fair allocation of indivisible goods, where the goal is to transform one fair allocation into another through a sequence of exchanges while preserving fairness at every step. Our focus is on the hierarchy of envy-freeness up to $k$ goods (EF$k$). We show that for any fixed $k$, two EF1...

F. Frank, Warut Suksompong · 0 citations
Preprint Sep 2026

When Maximum Nash Welfare Becomes Strongly Fair: Bi-valued Goods

For the fair allocation of indivisible goods, the milestone work of Caragiannis et al. (2019) revolutionized the understanding of Maximum Nash Welfare (MNW) allocations by revealing their"unreasonable"ability to balance fairness (EF1) and efficiency (PO) for general additive functions. Subsequent work established that...

Ze-Han Lin, Xiao-Wei Wu, Sheng-Wei Zhou · 0 citations
Preprint Sep 2026

Revisiting EFX and fPO Allocations for Binary Chores

We study fair and efficient allocations of indivisible chores under binary additive costs, with a focus on unequal entitlements and best-of-both-worlds guarantees. While binary valuations have been extensively studied for goods, their chore counterpart remains much less understood. A notable exception is due to Tao et...

Ze-Han Lin, Xiao-Wei Wu, Sheng-Wei Zhou · 2 citations
Sep 2026

Fair and Efficient Allocations: Decision Problems in the Gap of Polynomial Hierarchy

We consider the fair division problem with indivisible goods and study the following decision problem: given a fair division instance, does there exist an allocation that is envy-free and efficient? We consider two efficiency criteria: Pareto-optimality and social welfare optimality. We provide a complete landscape on...

Xiao-Lin Bu, Biaoshuai Tao · 0 citations
Preprint Oct 2026

Subjective Valuations Make It Hard to be Fair: The Complexity of Resource Allocation to Groups of Agents

We study the parameterized complexity of finding an EF1 allocation of indivisible items in the group-sharing setting, which has received increasing attention in recent years. There, items are not allocated to individual agents but rather to one of two (or possibly more) groups, and agents within that group all share th...

Argyrios Deligkas, E. Eiben, Robert Ganian et al. · 0 citations

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