Unified Fair Allocation of Goods and Chores via Copies

Yotam Gafni, Xin Huang, Ron Lavi, Inbal Talgam-Cohen

Research output: Contribution to journalArticlepeer-review


We consider fair allocation of indivisible items in a model with goods, chores, and copies, as a unified framework for studying: (1) the existence of EFX and other solution concepts for goods with copies; (2) the existence of EFX and other solution concepts for chores. We establish a tight relation between these issues via two conceptual contributions: First, a refinement of envy-based fairness notions that we term envy without commons (denoted EFXWC when applied to EFX). Second, a formal duality theorem relating the existence of a host of (refined) fair allocation concepts for copies to their existence for chores. We demonstrate the usefulness of our duality result by using it to characterize the existence of EFX for chores through the dual environment, as well as to prove EFX existence in the special case of leveled preferences over the chores. We further study the hierarchy among envy-freeness notions without commons and their α-MMS guarantees, showing, for example, that any EFXWC allocation guarantees at least 114 -MMS for goods with copies.

Original languageEnglish
Article number10
JournalACM Transactions on Economics and Computation
Issue number3-4
StatePublished - 19 Dec 2023


  • Fair division
  • approximate envy-freeness
  • resource allocation

All Science Journal Classification (ASJC) codes

  • Computer Science (miscellaneous)
  • Statistics and Probability
  • Economics and Econometrics
  • Marketing
  • Computational Mathematics


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