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Fair Division of Indivisible Items: Envy-Freeness vs. Efficiency Revisited

Author

Listed:
  • Steven J. Brams

    (Department of Politics, New York University, 19 W. 4th Street, New York, NY 10012, USA)

  • D. Marc Kilgour

    (Department of Mathematics, Wilfrid Laurier University, Waterloo, ON N2L 3C5, Canada)

  • Christian Klamler

    (Department of Economics, University of Graz, 8010 Graz, Austria)

Abstract

We study conflicts between envy-based fairness and efficiency for allocating indivisible items under additive utilities. We formalize several small, transparent instances showing that standard envy-freeness (EF) or its relaxations EFX and EFX 0 —i.e., envy-freeness up to any item, where EFX restricts attention to positively valued items and EFX 0 allows removing zero-valued items as well—can conflict with Pareto-optimality (PO), maximin (MM), or maximum Nash welfare (MNW). Normatively, we argue that envy-freeness (even as EFX or EFX 0 ) is not a panacea for allocating indivisible items and should be weighed against efficiency and welfare criteria.

Suggested Citation

  • Steven J. Brams & D. Marc Kilgour & Christian Klamler, 2026. "Fair Division of Indivisible Items: Envy-Freeness vs. Efficiency Revisited," Games, MDPI, vol. 17(1), pages 1-10, January.
    • Handle: RePEc:gam:jgames:v:17:y:2026:i:1:p:4-:d:1840130
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