arXiv:2406. 12413v3 Announce Type: replace-cross Abstract: We study the problem of allocating a set of indivisible goods to a set of agents with additive valuation functions, aiming to achieve approximate envy-freeness up to any good ($\alpha$-EFX).
The paper investigates the compatibility of envy-freeness and equitability in fair division, focusing on both indivisible goods and chores. It shows that the relaxed notions EF1+EQ1 may not exist even for normalized additive valuations, but provides an algorithm that finds an EF1+EQ1 allocation for up to seven agents with binary goods. For chores, the authors prove that a stronger EFX+EQX guarantee always exists, regardless of normalization, and they also explore cross-notion ex‑ante and ex‑post fairness guarantees.
arXiv:2607. 23310v1 Announce Type: cross Abstract: We study an online variant of discrete fair division under generalized assignment budget constraints.
arXiv:2607. 23367v1 Announce Type: cross Abstract: We study whether strictly positive marginal values restore the compatibility of envy-freeness up to one good (EF1) and Pareto optimality (PO) for indivisible goods.
arXiv:2609. 03846v1 Announce Type: cross Abstract: We study the allocation of indivisible goods among agents with identical additive valuations, focusing on envy-freeness up to one good (EF1) and Nash social welfare (NSW).
The paper studies how to allocate indivisible goods to strategic agents with additive valuations without monetary transfers. It investigates whether mechanisms can guarantee pure Nash equilibria while ensuring fairness, focusing on envy‑freeness up to one good (EF1) and envy‑freeness up to any good (EFX). The authors show that the Round‑Robin algorithm yields EF1 allocations at every pure Nash equilibrium, and that a cut‑and‑choose algorithm for two agents produces EFX and maximin share fair allocations in equilibrium, a property absent in the non‑strategic setting.
arXiv:2608.24400v1 Announce Type: cross Abstract: We study multilevel fair resource allocation with tree-structured hierarchical relations among agents. At each level, the problem can be viewed local...
We prove that computing a complete contiguous $\varepsilon$-envy-free cake allocation is PPAD-complete for normalized rational piecewise-constant additive valuations. The hardness holds even when $\va...
arXiv:2608.29097v1 Announce Type: cross Abstract: This paper studies the problem of proportionally fair clustering, where the goal is to select $k$ ``centers'' from a metric space that fairly represe...
arXiv:2608. 03171v1 Announce Type: cross Abstract: We study fair allocations of indivisible goods among agents with heterogeneous monotone valuations.
arXiv:2601. 17944v2 Announce Type: replace-cross Abstract: We study repeated allocation of shared resources among agents with time-varying demands and capped linear utilities.
arXiv:2509. 21785v2 Announce Type: replace-cross Abstract: Discretizing raw features into bucketized attribute representations is a popular step before sharing a dataset.