arXiv AI
Improving the Bounds on Approximating Weighted Maximin Share for Chores
Read the original on arXiv AI →The Flow has not summarised this story yet — read it at arXiv AI.
Related stories
arXiv AI
Jul 31
Pushing the Frontier on Approximate EFX Allocations
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).
arXiv AI
Aug 28
Simultaneous Envy and Equitability Guarantees
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 AI
Jul 28
Online Fair Division with Budget Constraints
arXiv:2607. 23310v1 Announce Type: cross Abstract: We study an online variant of discrete fair division under generalized assignment budget constraints.
arXiv AI
Jul 28
Fair Division with Strictly Increasing Valuations: A Tight Threshold for Two-Agent EF1 and PO
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 Machine Learning
Sep 4
EF1-Constrained Nash Social Welfare with Identical Additive Valuations: Complexity, Guarantees, and Experiments
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).
arXiv AI
Oct 23
Allocating Indivisible Goods to Strategic Agents: Pure Nash Equilibria and Fairness
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.