Simultaneous envy-freeness and equitability

Determine whether envy-freeness and equitability can be achieved simultaneously for allocations of indivisible goods under Leontief preferences.

Background

The paper establishes results for envy-free complete allocations of indivisible goods under Leontief preferences, including guaranteed existence when at least two goods are present and computational results for welfare-maximizing envy-free allocations. It identifies the compatibility of envy-freeness with equitability as a direction for future research, but does not resolve whether the two fairness criteria can always be satisfied simultaneously.

References

This work opens several promising directions for future research: (i) studying the complexity and existence of other fairness notions, such as equitability; (ii) investigating whether envy-freeness and equitability can be achieved simultaneously; and (iii) determining whether envy-free allocations always exist when some agents may have zero demand for some goods.

— Envy-Free Allocation of Indivisible Goods under Leontief Preferences  (2609.28308 - Inamdar et al., 23 Sep 2026) in Section Outlook