ARTFEED — Contemporary Art Intelligence

New Results on Approximate EFX Allocations for Indivisible Goods

other · 2026-07-30

A new paper on arXiv (2406.12413) presents improved existence guarantees for approximate envy-free allocations of indivisible goods. The authors show that 2/3-EFX allocations exist when there are at most seven agents, when agents' valuations take at most three values, or when valuations are represented by a multigraph. This extends prior work which established exact EFX for up to three agents and 0.618-EFX for any number of agents. The results relax the notion of EFX to achieve broader existence.

Key facts

  • Paper arXiv:2406.12413
  • Studies allocation of indivisible goods to agents with additive valuations
  • Goal is approximate envy-freeness up to any good (α-EFX)
  • Exact EFX known for ≤3 agents, two-valued valuations, or graph-representable valuations
  • 0.618-EFX known for any number of agents
  • New result: 2/3-EFX exists for ≤7 agents
  • New result: 2/3-EFX exists for three-valued valuations
  • New result: 2/3-EFX exists for multigraph-representable valuations

Entities

Institutions

  • arXiv

Sources