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.
By Hadi Hosseini, Shraddha Pathak, Lirong Xia, Chengkai Zhang
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).
By Georgios Amanatidis, Aris Filos-Ratsikas, Alkmini Sgouritsa
arXiv:2608. 03171v1 Announce Type: cross Abstract: We study fair allocations of indivisible goods among agents with heterogeneous monotone valuations.
By Thanasis Lianeas, Alkmini Sgouritsa, Minas Marios Sotiriou
arXiv:2608.24400v1 Announce Type: cross
Abstract: We study multilevel fair resource allocation with tree-structured hierarchical relations among agents. At each level, the problem can be viewed local...
By Maxime Lucet, Nawal Benabbou, Aur\'elie Beynier, Nicolas Maudet
arXiv:2607. 23310v1 Announce Type: cross Abstract: We study an online variant of discrete fair division under generalized assignment budget constraints.
By Saar Cohen, Nicholas Teh, Paul W. Goldberg, Michael J. Wooldridge
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).
By Zih-Sian Yang, Yi-Hao Chen, Yu-Te Kuan, Cheng-Jui Wu, Chuang-Chieh Lin, Po-An Chen